Best Known (110, ∞, s)-Nets in Base 27
(110, ∞, 324)-Net over F27 — Constructive and digital
Digital (110, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (110, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(110, ∞, 325)-Net over F27 — Digital
Digital (110, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (110, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(110, ∞, 2923)-Net in Base 27 — Upper bound on s
There is no (110, m, 2924)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (110, 5845, 2924)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275845, 2924, S27, 2, 5735), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 52796 125198 888918 832201 317227 351602 825225 275330 542600 860453 833489 531873 555806 283219 596180 302946 017361 964034 733577 761831 985348 595993 624034 884299 758818 288483 437651 600002 653323 232597 424787 048287 180574 786573 201579 747062 356981 839444 956991 430269 260042 376120 666950 003060 044574 543036 044565 784512 386385 338297 098025 897906 783882 937324 032615 569369 219349 920837 418482 317133 837193 589228 042140 607476 290300 961898 384935 505621 255488 976859 996130 889129 895696 026640 999636 518786 661835 546254 086391 014837 574198 061689 368761 629309 422539 138261 289553 485588 667369 715235 021935 806125 359871 931249 321766 171529 390843 903217 020504 790119 773411 358197 142503 379630 574281 806110 159830 952736 591829 288569 158333 088941 869765 646041 123271 817197 415400 129448 209776 388689 349483 905161 420286 673323 496381 827409 394183 676857 702265 317146 641116 060150 399334 975561 585967 120911 064723 592876 140914 263179 623048 813876 964824 032819 583460 695353 667515 379672 097850 394323 891379 727605 452460 614020 986768 458911 419002 570775 100308 911175 077852 092786 160269 110850 670181 031106 908809 386721 443711 776627 737110 394289 573474 601577 042551 694989 365682 126275 227817 128936 200172 033034 450319 700208 036489 487937 142527 529042 415158 757179 556607 071671 383860 813215 417556 141324 717802 559181 316480 162288 763492 480131 360740 424141 021733 287425 651636 164419 354401 024120 841309 076072 737730 556887 979181 731675 830928 975164 817015 652821 291576 060450 491644 449967 243519 921279 233288 221732 427054 390683 058220 436070 816195 964121 671303 851141 151743 582114 873534 056595 385823 075067 655688 567494 278598 169357 488717 598600 617300 959147 413927 974924 912145 761930 242427 424802 686763 614912 681515 583760 994964 225046 353392 266069 383495 320025 987265 431011 087177 961710 239669 420590 300210 435026 174700 757060 240085 057963 757322 705074 122214 437225 733987 094418 729148 979136 678023 453228 544451 588942 398757 150756 605696 182405 472197 296418 847615 635705 564783 261122 492657 838055 449589 642859 618807 385744 603819 305838 217626 281178 317691 377803 664357 841555 163613 687740 948542 539105 243638 749356 276204 581035 230169 663676 996430 447588 798575 489160 104424 565982 451791 080427 768404 439190 157002 703753 794113 340473 341249 068177 390426 598823 238433 523415 021714 427312 935506 604042 619946 188373 176553 455031 635513 653602 902727 555955 593138 335900 428528 855026 597873 429584 084808 875650 306632 031462 400632 537988 158815 989632 970723 737007 152941 589994 257749 396594 303053 158479 490372 376210 092644 081351 205061 654036 470404 635520 447163 779010 255847 056123 433740 185528 371721 331604 287487 340342 884932 566301 487850 481097 973517 419515 416781 490868 613928 922219 254854 168994 027427 139753 718909 726201 574744 933211 875887 487432 617760 497768 845397 755198 000608 719894 503721 885075 415380 709447 684683 837824 519181 564102 029135 934647 409124 706463 221881 806682 167794 620991 728627 283266 489598 220050 471224 612478 620580 834992 733096 892029 236867 690790 299879 307662 810574 212794 955072 394064 332004 762021 743942 675412 701232 419115 854360 600664 313490 570321 296535 401285 939292 147698 447486 482430 392053 699789 656825 071454 971133 314877 044160 519805 257476 371275 734215 800607 450358 367993 636564 492999 069262 433600 761701 248031 762712 569837 262539 528184 751468 556649 941732 536968 868741 457420 618258 116181 047552 837350 956708 506320 335040 166325 412771 277971 427530 523414 495252 174091 638220 050555 697076 112644 410712 035747 099295 033830 997728 317461 047991 834189 056405 172539 165284 368332 707105 443465 820704 411119 025647 700275 812759 432361 959085 196079 620707 893312 865770 418895 161160 183252 471610 591569 278869 762557 226700 493131 737557 458265 300023 164072 885766 256988 344678 887872 147475 378632 874735 014098 602078 727661 121713 609544 403658 162989 865856 507260 376666 232269 627896 330803 331274 649100 163847 865822 409845 216978 597462 378436 114682 121261 324910 937676 534344 374462 502814 719665 455542 176312 974649 489318 372217 497376 815387 331823 864180 146248 253530 744909 848335 977281 723652 849298 206012 065475 212079 501940 173682 643325 811252 529577 094708 525584 515414 792557 858001 988014 993479 432870 559953 201369 374511 994846 340005 730272 807807 322714 027314 716474 679852 739504 292116 611377 752419 982898 775384 889527 640367 474929 828091 341505 289270 912103 569133 722613 827944 299881 455988 630419 733401 141604 640339 238485 897741 035508 133356 344018 214443 318868 513702 165678 367180 640257 972429 624649 199665 740671 084492 286041 475927 648596 042355 471987 311588 640106 228245 778557 307182 856492 286544 942882 753065 892910 702351 803127 521835 710423 483771 822322 260065 706144 898183 699515 641574 263571 841479 024626 121628 640824 181245 629102 432820 037374 017496 739340 376145 517241 133368 026867 611153 237028 987755 618768 950992 827971 205309 300021 997909 923706 978040 235114 819126 157335 361964 512073 929162 285083 201850 540672 316453 350634 834124 472444 828014 415137 089099 548767 826027 376936 678092 611103 285063 805583 832937 508042 612541 474217 731755 685749 298127 034237 269915 022801 659940 541034 840754 933386 371781 147790 257975 022216 304059 516885 763660 240312 448246 237768 702917 945570 134181 292902 783681 758999 205877 805555 686089 837087 195809 902145 781154 781854 416732 887935 190239 485914 586656 530338 999142 395059 444365 167356 558404 612382 908289 849603 636337 555254 150777 766386 219283 676864 633844 720177 339395 003506 885861 674998 920548 359893 492342 230694 373868 036749 398590 054304 223242 210521 593313 504306 192652 309311 745596 432826 542056 547160 199896 439918 550443 505891 692242 928552 718496 696933 651267 570403 287552 196015 306515 755680 331231 535657 345120 336199 379472 461024 942083 823972 942428 301911 564786 082457 722880 893718 543599 188514 637152 534784 034487 228761 224756 115299 522159 730701 448977 841936 510900 563319 989486 960003 207877 279174 360493 673618 956109 779411 360797 209032 113507 982313 512761 904099 830911 234581 348567 191253 410362 719864 798184 886342 989561 566156 371571 564357 894585 230782 793182 333675 533275 034388 075418 275279 822224 094778 219903 015263 714245 062518 058543 640383 065222 775313 446427 155073 164787 242661 874757 206884 347012 838605 849849 717667 803874 361973 603168 098805 175443 555828 633924 877349 536603 243115 926571 354194 193230 510300 744605 954162 289099 123543 556975 928228 059445 558437 415685 650455 923507 462383 467163 334599 137080 377221 666144 245467 876021 796367 503085 599397 606980 522109 271226 168734 006709 342411 085229 161365 643719 587199 851020 664976 719390 440620 593538 511203 639944 971236 291011 368773 735589 279944 246609 188940 856883 925212 316496 281854 414787 490804 205643 878166 962732 193338 071225 575160 248684 960837 468560 603958 830124 266190 465973 896565 268222 028018 718484 389077 848759 312481 144929 582706 106512 536243 192916 193132 289556 057160 847958 255585 430724 966662 217139 578915 954749 342225 380407 387076 544644 798832 300617 702666 694198 024003 835430 352490 154692 912944 911217 319072 519124 624358 813535 316983 925284 403713 094354 389536 717829 662792 713840 857377 068711 719016 618393 312957 055937 828714 287865 381042 792474 786038 989793 891959 006129 083210 907833 912430 185488 111847 831553 753307 298098 839585 946649 186549 954905 927746 695741 021107 372810 096973 682644 236762 658190 564819 075514 991881 167984 304793 194832 747818 383299 352427 036813 843050 100035 673624 085580 616685 910231 264697 880219 987787 906576 655551 271886 265562 226334 014621 063745 638071 231105 099650 102371 458034 887894 119878 585816 286818 989861 493202 793530 573850 331926 613751 557195 450158 888901 655203 498089 683544 893268 446074 388476 460699 507838 998712 017781 446006 129418 534307 896164 681080 651998 174644 080334 785392 982159 813928 984918 270835 650702 470598 345081 453112 491553 288227 870526 031447 814905 059694 992738 833591 112546 492564 501474 149364 680563 366233 431686 225175 174637 119078 452671 317228 485591 406393 656777 858992 989117 981194 052481 139999 648410 159228 025120 116511 003302 217216 945240 790517 630259 284581 941837 160847 559163 087904 790471 256721 379502 185967 953324 985771 664690 272601 842555 182148 205480 179740 417353 631660 573205 196036 542549 420114 296607 368100 383428 748310 956304 186487 949586 014788 060888 700390 284439 934426 220130 409463 328062 668406 020962 754729 992653 800676 800650 251156 312351 893777 058551 693548 422786 484970 649118 941283 921211 778536 547823 948073 024303 141487 327174 715730 455499 123571 730156 998217 265614 918112 056127 645840 135555 368767 552885 932920 199152 911943 694262 496809 793843 236795 402477 957930 656453 031520 397532 361283 732818 623315 999283 131842 327779 556498 719565 499299 843949 151062 755065 497042 955602 636557 815651 868916 186981 022015 990231 413471 749238 222390 411254 782714 722848 449410 970907 043248 387558 340805 371273 577230 730540 733459 898902 674372 588903 666732 248026 391047 857047 627631 238212 965120 490492 761923 742703 603947 968684 395915 088364 793476 271662 110110 895278 698616 117748 239025 417842 490199 859385 101510 671501 929560 426180 221087 217943 792118 273300 956488 636425 837985 232046 873050 487689 180567 893664 983837 952210 570433 516262 897889 664898 122564 930325 458686 096627 386831 654397 879488 624073 588359 992605 342441 869472 135275 979971 759672 976014 948665 671776 612442 174692 397069 568660 829631 608660 593250 329831 428183 265938 340529 326164 / 239 > 275845 [i]
- extracting embedded OOA [i] would yield OOA(275845, 2924, S27, 2, 5735), but