Best Known (101, 101+∞, s)-Nets in Base 27
(101, 101+∞, 324)-Net over F27 — Constructive and digital
Digital (101, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (101, 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
(101, 101+∞, 325)-Net over F27 — Digital
Digital (101, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (101, 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
(101, 101+∞, 2688)-Net in Base 27 — Upper bound on s
There is no (101, m, 2689)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (101, 5375, 2689)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275375, 2689, S27, 2, 5274), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 42109 489403 429517 882979 225764 262227 467608 389707 200081 978062 733657 538713 170956 682958 677708 201054 237667 823539 755184 078382 232714 798354 769854 103582 671346 681746 721127 054313 705605 271507 896935 282576 784303 343425 332353 664329 077244 474244 070595 361216 142389 008462 717734 796633 854204 523506 449244 378792 436833 975009 241013 686916 661272 266645 850557 406360 548251 207982 578768 929584 829980 126376 571770 186585 368638 982098 944217 651256 362158 358421 718262 432672 260643 464549 327229 868649 207554 681224 608549 762482 252408 266329 251650 982869 844977 779837 120208 357724 968258 238060 473565 933538 026286 528281 245837 146523 913423 622634 581292 041287 006781 433484 727856 319807 122360 951598 565174 678835 322512 752107 969054 405740 204389 151499 935728 781488 662855 445052 821889 316084 771977 915869 312550 864794 799884 414844 971696 067403 895076 991094 930945 292809 991779 848178 196507 399065 073521 079409 956094 901173 509728 907167 663440 052025 329965 451649 515386 396769 092958 074847 122581 469366 132943 210207 101131 192011 647887 986513 418395 010557 747812 930834 200373 629612 520471 676488 867480 304862 252170 797829 081849 096112 653488 496450 831118 891694 414500 427244 491069 252486 663059 019166 040776 915501 513281 528248 834056 507531 284546 147619 988406 593983 147603 565134 689929 938536 732372 094606 002784 368654 040254 528424 462930 783416 517422 913511 532263 928870 302076 195500 786867 020692 284973 695202 539620 839831 997373 908009 961462 525699 029165 613025 321284 673801 568192 478253 642687 760262 574641 780594 481633 019705 640750 050890 675569 231907 058936 622144 004694 732133 235079 005500 091407 042992 208243 154291 928985 341483 428549 144537 079856 550028 397904 283273 830575 320366 284815 668134 728040 345796 259037 182620 613728 985921 514013 120100 151741 104838 826799 556609 212106 279874 789376 957045 490286 895789 223291 065677 599094 337789 699623 627651 948551 485439 101016 105496 734907 393435 116916 958374 019026 378913 137585 116333 454149 828293 936619 164598 396277 122176 355435 120880 030679 370278 044939 269702 936082 266289 283665 975306 381486 287997 124495 767998 731184 832249 390033 105334 458640 275718 022247 504500 577254 164339 349831 482289 539460 507469 080960 993279 644740 409783 501390 626608 756478 642542 598036 922720 813478 020505 592819 274941 637270 089545 072411 139776 238639 588983 067420 546466 226973 966671 872439 576240 324890 229108 179344 788384 633192 815761 737032 340080 693214 186548 090978 520986 383646 365105 874324 660282 339850 298962 788766 239386 435790 509756 946962 974189 921481 435224 826153 369528 337110 533149 345196 960263 763922 183344 901161 161585 451994 029279 114051 710315 586360 850424 144562 995177 108334 305419 371528 508579 108470 821579 549792 547457 231723 927764 908235 080444 897952 423613 445347 850239 221299 948629 920610 894476 949725 320464 172451 941373 591097 559706 020146 408906 725129 825626 109644 929311 147804 220176 671492 960395 109974 426166 820500 695873 760627 812921 116222 731336 450168 508894 125652 157825 022773 972612 945301 253033 208367 661001 959394 925687 607581 861475 199639 540371 301353 395653 614184 811705 536550 656190 845832 602674 563021 240852 078397 964960 713929 436427 843144 087250 899941 237202 710364 239200 139253 719476 477392 302372 025456 711046 857747 211075 582533 775402 581028 737780 437572 408953 624462 127811 003905 595680 691843 478857 133631 952423 626006 073941 038882 710919 313295 258482 313811 418868 154617 764722 103339 902854 117916 449398 001760 799532 008750 886763 766245 289243 416794 697867 990699 513846 859357 802310 281559 682602 813419 624797 647255 355511 086997 029653 982315 796473 975132 327935 640616 514799 921020 517981 364517 512831 286170 072277 068278 740796 234503 167767 490533 173909 086692 939045 857464 538332 238121 391817 553133 109309 084521 430020 488969 716296 843200 245728 991600 224604 571578 520465 092186 869389 249436 189911 206793 414757 015475 718495 499429 187102 802987 567389 474966 844728 370901 106814 953921 422569 906628 506792 814814 970197 763930 175889 588222 808540 994724 434556 568606 611503 070494 109004 972564 587702 349642 330595 174270 779134 064314 852656 980293 180685 007548 278082 870139 141140 069703 546774 947947 134923 320534 909617 004322 361146 703491 167751 785722 707994 374822 983797 927971 007377 058304 618212 370096 542670 374665 872431 948180 810675 856991 664943 082675 315177 035915 546934 030374 002719 652468 999534 310116 712242 128429 962094 465228 829009 912146 493843 458360 875028 962338 376972 519981 799194 995429 253355 721438 150214 602749 775429 413050 090797 382561 735192 784885 195312 605502 933252 995390 746485 824408 507437 878840 709265 041827 884038 091688 444175 088244 384198 475364 453111 353760 801872 212320 651668 048246 737376 960385 121591 639033 927091 088593 560217 030874 237014 871592 557561 451661 225284 838631 536808 811477 612935 206058 268281 212657 361120 269194 761595 995841 316257 879776 320546 499890 838931 471502 541456 679277 013145 366871 745873 239887 214326 421395 028210 707712 834612 104976 341761 335452 171039 964282 694304 162629 872071 070249 041381 318401 279934 612433 971437 629121 849800 865299 286311 517028 871555 302399 532952 328029 674428 899858 650092 930485 573838 500613 610492 562473 418008 174114 797234 079704 073345 993385 332018 386626 489201 963456 598890 271771 399065 485248 665195 543302 283325 845516 080923 979720 714286 623013 048103 317699 428455 548357 307597 914899 116076 164894 805386 181508 775899 185600 284994 473279 694727 519333 026716 418508 306094 407668 604777 817346 658560 504645 747237 343451 818515 347653 126711 896543 571530 661001 660405 821054 152941 446526 063260 993028 711510 480906 575109 078012 754620 016305 322979 419220 735049 286058 806626 972833 874961 299992 036047 536280 567465 524430 454380 191980 792634 656777 889812 103122 442788 845479 599217 570359 649702 763868 804799 947220 489098 516781 681349 942008 926024 977752 270235 956241 262854 838111 117386 340080 913841 092966 517644 167631 477425 766701 479181 651085 997636 715386 826364 056971 626991 926341 716227 457475 224305 857956 932100 538129 844147 681222 417500 900762 992995 350754 685939 552791 044414 631495 098341 346541 418777 996224 544850 004960 344538 376783 079862 871978 544220 248737 972052 541536 034372 238358 939514 264629 849456 044264 004052 852355 101581 277130 745770 460945 730959 143231 429567 299526 593882 367390 423807 160925 200681 330689 790860 012128 555319 362361 447775 520612 358381 208984 051330 748593 000197 425919 088892 869565 549494 514052 045202 401301 334927 684736 708281 015859 003836 477631 595378 292473 365022 353492 202776 053527 222556 049643 105681 139827 176221 950512 280089 956242 344196 850942 148218 657892 468158 059758 965914 584980 346713 455348 153040 096479 177793 121521 759155 307414 654110 529398 457988 833855 444449 720605 596131 836398 288997 599799 409657 037701 178827 755039 766244 056717 102895 692740 100589 412685 232833 102689 370550 806691 988007 725155 335599 725726 580647 225232 628583 984745 372668 794703 152254 690430 171633 579527 841035 950767 608763 411493 800986 966816 571041 900170 508577 004462 784261 002170 007491 553579 236946 210304 092320 169351 846421 726680 257479 810220 524068 254520 333452 899222 734123 453761 645509 189733 152526 023826 365576 089397 501355 564716 217233 169477 181111 016266 976825 245549 641537 631308 871768 660843 212785 169384 748478 082382 136054 487695 333038 995662 928650 231012 586954 017187 472151 716208 355693 899831 632206 224534 470197 319810 118322 424924 469300 603826 972980 979777 377757 750418 910963 001284 804140 883906 830258 012316 500866 042462 263822 752063 641145 548446 111062 896464 373181 838041 980836 464799 454814 922504 446412 304386 708915 728685 998675 657967 053585 217261 352351 283842 488800 661573 629647 830799 363870 266202 212291 646023 830257 129106 198067 788474 551910 266286 813212 223655 792078 929099 360967 131165 913139 711752 664762 097167 554045 845739 322897 535148 405430 281487 939389 977682 337312 884577 102082 377065 402728 243682 671610 832542 675114 754221 678258 994237 707524 014473 430980 076470 562908 608404 212124 603552 963561 290527 297302 645977 271812 702676 685523 486639 096430 520694 758541 834288 313168 029256 400063 242341 713510 293623 965322 378548 155463 975343 457806 412522 680404 370080 838807 653962 510460 498055 821493 238358 768306 550740 663794 062776 823571 931108 668026 392319 124941 087916 141947 164664 121455 020545 345356 668557 309621 014600 467142 086044 332923 677795 813203 606341 450820 840083 166192 699383 060217 305880 574033 601394 402250 034390 374367 734314 188313 557021 997525 819348 024486 978128 753621 109751 858546 991407 617725 850559 262650 113280 021015 235343 908344 002681 742640 731395 943472 642773 150413 911883 108993 290306 084564 495401 / 1055 > 275375 [i]
- extracting embedded OOA [i] would yield OOA(275375, 2689, S27, 2, 5274), but