Best Known (102, ∞, s)-Nets in Base 27
(102, ∞, 324)-Net over F27 — Constructive and digital
Digital (102, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (102, 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
(102, ∞, 325)-Net over F27 — Digital
Digital (102, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (102, 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
(102, ∞, 2714)-Net in Base 27 — Upper bound on s
There is no (102, m, 2715)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (102, 5427, 2715)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275427, 2715, S27, 2, 5325), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 256087 498398 923644 964059 445427 566257 706749 027740 111422 251658 765906 478585 138503 917451 031601 239497 100435 870651 792757 299358 433873 520037 879671 273987 820937 358895 862847 828565 395678 396698 550003 884647 858342 512383 929550 877359 103023 601555 552704 469165 595361 241502 651658 430809 017397 147460 466566 826295 355326 217612 411940 967760 365634 205809 166552 565528 503887 705336 845717 847404 489187 326230 443616 738068 090330 475177 464605 175220 212478 630834 263326 732599 505904 822281 184094 708423 944696 363744 059797 482467 406972 636091 234960 683220 152620 630943 649613 192116 176825 189399 889153 288753 573482 057377 823462 577274 227614 430350 744070 030141 385245 350872 109363 424356 777331 599221 891003 363264 260489 620621 573904 587840 990231 607893 518543 451564 985054 748002 144194 360376 008603 079893 671332 033699 481158 787433 692669 808125 718329 308708 770649 590991 460787 185492 922238 675689 527045 726678 857214 888709 741237 300204 272515 293442 737939 245486 053009 626453 344115 169024 205913 164764 114759 972948 277494 666421 628375 664895 667971 533701 915079 437063 412295 219775 898049 612582 102010 322901 564458 065865 723587 353288 903845 068124 583920 693502 693907 704981 316088 637918 357855 639239 353452 302814 605951 992701 350708 356201 022231 267128 030121 411190 990241 837327 250795 166129 141244 537506 000391 571306 315172 574638 407210 064051 072832 508999 196699 141256 086630 089610 617307 563997 339806 003193 972956 755725 499523 222200 338590 962088 676801 033993 416762 405773 749217 254575 306452 477208 354484 344189 665683 804444 514383 045064 830824 219267 920173 169085 371695 524456 045201 504828 444770 410547 553121 509475 193920 280029 582530 844988 728395 910328 571515 751733 534940 572021 726787 501543 655605 234855 954928 972755 536303 859035 533151 298635 545648 720173 361599 306758 040286 892159 218217 079101 547915 857027 525142 580653 333068 338226 469890 132463 279483 193909 001886 847957 963046 464782 338782 202170 962882 423509 312187 608474 787461 840766 954886 584555 655669 303952 547182 064643 899042 890845 081054 004370 935764 284845 682277 189964 358685 320449 777238 218769 205917 398361 741415 538597 271331 999291 656987 332687 622290 750944 895311 435873 053583 430820 161854 052149 700139 173138 820044 736811 024104 165661 328081 024748 829220 510964 688492 632450 021113 716250 445115 622963 928759 264234 910714 492956 647463 752910 107835 621751 730298 667419 288344 902363 753100 216596 317325 089561 212814 392860 829556 273215 541718 521031 345613 096426 011223 308718 821954 362747 660771 429007 223373 556350 145527 795009 904635 453178 182856 230614 088377 661270 591950 382354 722699 116375 206141 088801 401223 436087 990387 803191 135180 219287 562353 051965 102471 449930 730867 830178 825767 675119 076878 813969 735063 260930 523420 672466 172389 585476 723182 678519 829885 169059 460360 632733 504600 941145 363731 408997 305763 767921 303521 553052 529835 708142 633925 611308 779755 348432 816430 740059 235855 013171 161070 199143 173103 281745 572426 148179 877351 387967 418147 945071 627503 370396 522804 360710 005947 274005 198925 456242 497155 064334 029321 056546 134078 826712 406302 597158 593893 766274 426655 860481 049150 415636 988258 144420 648684 017698 432298 048707 521378 673195 430105 451407 602319 819548 768151 709037 476849 911874 067637 810006 180587 392826 245750 442489 752035 099043 423586 384235 056762 805417 700796 125904 035570 588447 593183 104383 951188 806369 835380 525381 946925 152972 034980 447569 284373 868524 653208 342101 442420 744775 204960 640312 686836 584951 596082 516762 013993 969004 441913 358439 239595 952121 584761 518615 455203 245169 510014 808202 110749 587663 436448 633297 018150 636904 020407 578401 883783 642908 687455 197881 433800 420040 519621 770716 358950 771096 952704 091742 255796 018697 253202 047690 344872 361973 042468 213482 351574 488071 360182 340387 309614 514745 911980 635969 631486 506397 710039 039716 898752 742119 244767 822214 845169 595727 704489 164280 961812 302419 021399 014420 394490 455342 252585 333281 640198 087897 636442 050274 631101 604186 145279 031491 037597 543544 245520 236484 150202 329172 702773 071491 176912 917473 059372 890847 133379 410893 236722 560123 556853 459217 528517 020463 668172 217444 128686 356771 910565 491341 812968 683636 253816 475287 533676 867369 831908 217756 416071 203709 601309 339147 746184 448002 102550 535404 499752 707623 445816 421423 470744 330999 860978 961482 906457 628138 575678 343967 124746 913087 339505 782503 749254 558084 993584 920225 157399 659477 922555 364918 441527 971253 517043 405591 801709 170998 435356 927231 679317 684497 066838 622795 217592 446201 750612 200927 956769 367443 915848 579668 736158 584926 232466 921271 882587 527215 294794 377615 592707 592312 339441 381301 820765 789171 226399 390637 306330 267624 517524 064780 109283 900179 213779 682307 559576 661313 927451 760462 547840 195601 046205 299762 907866 922861 399634 011114 293973 987425 430343 798980 882140 213592 601274 703696 463434 775091 919153 531872 482454 418916 897799 300259 671011 508903 232457 461837 466643 924343 629663 234780 218215 117000 584901 210613 780591 770414 021874 639128 730945 079235 845633 700334 886916 527879 768713 956219 733802 381602 702798 344420 097406 070730 614798 086771 324031 423182 644576 821405 145379 677006 495330 835261 033577 075967 335595 090293 483899 993233 485237 859944 102928 190551 007676 240193 231568 140143 260300 748613 210846 687735 884118 500695 686608 515866 242438 482296 413768 627480 898204 355216 348709 682236 761886 274948 491806 532551 054213 910587 414922 485103 589467 663153 614226 491939 273475 183417 365719 780380 898263 770568 717725 408622 158712 636539 032534 845016 422196 301481 361948 299822 098401 077121 764561 380130 056397 592157 876775 184485 043152 906598 396464 720605 630244 415979 690065 144521 116810 002545 307658 639329 345087 972924 914573 753697 404477 704864 157626 028929 526987 241780 533252 841516 624199 517675 270633 568779 837177 691427 657276 979903 191864 514689 817995 694486 675870 294746 394550 307584 725352 111668 540648 641561 974825 604909 234064 085702 022062 738395 201999 534851 370049 665099 877775 790744 293438 532965 055366 693509 122372 362966 108665 991935 554041 870352 626546 507510 212974 782434 536212 359935 343581 911428 665219 074075 287429 080317 384224 484669 126655 492175 731581 434970 549091 791490 332867 820325 158294 605893 274223 452460 510578 626856 117219 217996 594459 714097 289039 816769 352671 698608 330610 554486 132489 210759 948131 033390 283336 370838 467924 118283 649913 071775 359704 564205 325397 472867 405598 410448 774601 939347 726851 404024 104392 463008 641687 434933 648205 953454 358479 368287 424651 170098 191453 260935 257037 286574 573240 938473 995152 472903 888576 098139 185388 644166 818027 593020 093928 450738 805259 678865 806714 280190 030037 570897 508660 990656 948638 008373 973601 027707 101450 263473 351673 548269 095871 100794 499924 019611 396347 364336 453659 408594 060406 883647 235641 546830 257859 946903 025798 928813 786006 924395 991566 881943 008135 010043 882157 199721 126213 535611 488370 157493 639515 731798 279279 123684 366565 711050 548606 925411 269904 805953 176764 292563 852906 617033 972095 263068 401541 364014 574730 028070 627100 780437 977459 391079 449718 913325 179606 753805 057429 393929 303121 026764 037244 811433 198958 125675 339755 830658 333780 558204 194702 554233 499262 992346 327783 141021 483441 741288 293452 848408 518901 581754 028854 388495 889493 278055 239888 696637 736262 838123 389787 531632 806101 811896 643374 469537 852536 101949 275607 038108 326385 931520 575708 861803 146289 083996 450916 439130 341286 759830 213665 470114 980173 666708 012438 155849 948723 814548 942179 201969 898498 197314 161783 178210 242583 293768 243859 622402 873616 646127 412521 318602 802507 866076 861957 532845 842952 260407 944453 942194 267696 987285 044531 009498 330696 471239 098357 532791 208882 672295 377070 547660 925585 135438 859173 126924 849323 422988 010430 702718 568147 455677 974633 777656 573881 843022 302453 066289 683642 572266 758274 979393 584401 295609 869475 248368 790448 031348 823936 370463 463307 406669 878662 364617 093702 263731 761682 456672 174447 305994 741268 521683 991288 365143 174292 903998 727716 538032 458063 387354 832792 896095 160038 298870 338273 097406 790106 434237 393329 200628 992873 070408 102061 120711 676248 281744 533028 666553 867961 185684 692800 141262 946038 587400 041233 310258 094381 203348 254371 160895 383201 156792 866238 443324 448558 987288 567372 727152 267196 867218 551581 743790 528444 633888 072068 203073 602004 570210 525884 577056 637895 785249 828045 054925 846398 821975 820152 718026 578951 595814 642874 821690 666374 207521 822378 629899 584890 091754 534158 681582 515875 471666 558445 492421 129935 296604 577220 560644 700256 229672 611890 967784 162450 253648 292937 419465 347462 / 2663 > 275427 [i]
- extracting embedded OOA [i] would yield OOA(275427, 2715, S27, 2, 5325), but