Best Known (53, 53+69, s)-Nets in Base 3
(53, 53+69, 48)-Net over F3 — Constructive and digital
Digital (53, 122, 48)-net over F3, using
- t-expansion [i] based on digital (45, 122, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(53, 53+69, 64)-Net over F3 — Digital
Digital (53, 122, 64)-net over F3, using
- t-expansion [i] based on digital (49, 122, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(53, 53+69, 298)-Net in Base 3 — Upper bound on s
There is no (53, 122, 299)-net in base 3, because
- 1 times m-reduction [i] would yield (53, 121, 299)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3121, 299, S3, 68), but
- 1 times code embedding in larger space [i] would yield OA(3122, 300, S3, 68), but
- the linear programming bound shows that M ≥ 81 482322 949596 735108 120931 138064 657435 165906 281684 372249 103100 981926 500725 461931 140027 869815 914152 435183 780326 239451 529067 167253 163470 716424 702277 607012 062264 280740 795377 516401 016998 026650 770434 850609 273812 522484 697771 939079 459217 462703 773452 856140 345345 318484 506945 314483 030256 488752 721472 003054 532652 056421 626795 711672 436241 394831 549065 690357 787805 951089 788493 327882 772502 594254 595744 442337 309658 515823 765071 489188 836400 959390 320558 688141 399533 736803 447410 974711 557749 225090 940317 681098 664515 475174 692926 893700 208038 594389 497111 205883 832830 831511 117009 846007 495449 530817 576960 / 3703 551056 155170 222412 326071 631519 548038 028745 756691 694145 945904 955094 772641 792674 070660 764846 177517 107480 271398 580675 096206 043857 172684 154626 873536 263622 423856 658315 837058 321694 027988 672294 391134 515688 556709 983512 010323 708665 523812 826767 000848 387193 425878 214198 764873 098436 841046 582901 659851 880568 220193 058868 451390 247886 374386 205373 244130 267285 120914 476848 623807 601583 541014 721603 972139 164648 514776 232984 725452 502935 063444 285995 042221 818472 233809 914116 607471 207078 590999 945646 705528 750212 716593 081425 779056 625908 094531 > 3122 [i]
- 1 times code embedding in larger space [i] would yield OA(3122, 300, S3, 68), but
- extracting embedded orthogonal array [i] would yield OA(3121, 299, S3, 68), but