Best Known (92, 92+∞, s)-Nets in Base 3
(92, 92+∞, 64)-Net over F3 — Constructive and digital
Digital (92, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 63)-sequence over F3, using
- t-expansion [i] based on digital (89, 63)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- t-expansion [i] based on digital (89, 63)-sequence over F3, using
(92, 92+∞, 96)-Net over F3 — Digital
Digital (92, m, 96)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 95)-sequence over F3, using
- t-expansion [i] based on digital (89, 95)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 89 and N(F) ≥ 96, using
- t-expansion [i] based on digital (89, 95)-sequence over F3, using
(92, 92+∞, 197)-Net in Base 3 — Upper bound on s
There is no (92, m, 198)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (92, 983, 198)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3983, 198, S3, 5, 891), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3316 945987 684569 906826 797981 970138 713335 809701 678137 159571 605924 839141 371846 745984 448015 399265 037415 790676 739147 268357 430585 783638 825053 422337 488012 800301 253955 742281 076847 800296 463826 286053 306072 584790 202709 533867 676619 645136 134743 239773 052396 751911 602620 493150 962118 480501 264541 849790 330981 534494 368170 617447 703040 798087 439567 556632 646930 131268 397693 779488 692339 941761 291397 941166 741034 947169 276459 309839 790530 956246 291630 527441 141221 062898 376328 044859 497537 457011 917548 / 223 > 3983 [i]
- extracting embedded OOA [i] would yield OOA(3983, 198, S3, 5, 891), but