Best Known (29, 29+42, s)-Nets in Base 3
(29, 29+42, 37)-Net over F3 — Constructive and digital
Digital (29, 71, 37)-net over F3, using
- t-expansion [i] based on digital (27, 71, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(29, 29+42, 42)-Net over F3 — Digital
Digital (29, 71, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(29, 29+42, 152)-Net in Base 3 — Upper bound on s
There is no (29, 71, 153)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(371, 153, S3, 42), but
- the linear programming bound shows that M ≥ 1 055633 583684 412124 576484 170255 131218 780961 470521 927693 463389 568320 189199 289559 169330 933131 798207 551957 567481 144539 850575 395329 102764 159939 358868 077128 618402 122131 171260 366925 398215 527745 180439 670326 837896 090390 666310 679248 321377 576820 431328 275321 422069 606660 949118 551478 240579 301418 914961 095796 891840 / 138 376916 366765 245149 784082 130406 254967 569712 303599 812312 770276 538679 404780 518662 697999 679212 679952 906967 837259 967292 004231 340859 946531 558376 639875 802868 726402 799726 504048 508110 636251 941347 913705 438595 007008 728154 695053 276605 319416 010222 452132 016051 115790 666606 828591 > 371 [i]