Best Known (96, 96+∞, s)-Nets in Base 3
(96, 96+∞, 64)-Net over F3 — Constructive and digital
Digital (96, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (96, 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
(96, 96+∞, 96)-Net over F3 — Digital
Digital (96, m, 96)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (96, 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
(96, 96+∞, 205)-Net in Base 3 — Upper bound on s
There is no (96, m, 206)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (96, 1023, 206)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31023, 206, S3, 5, 927), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39206 144117 807104 570960 774189 410991 763668 026562 292070 813816 877830 818299 264812 851379 149337 338574 417608 149220 331870 304891 601416 340732 176890 151041 890383 194964 667990 133602 397570 998574 737094 955422 449985 040894 309901 535323 727307 179355 141295 764816 331640 346820 011000 605919 854688 223164 086152 011769 888753 321753 123301 249537 519781 486711 125175 341193 819406 402545 868308 401974 901678 185417 889466 564470 450549 452391 718475 958545 023777 257701 097153 135725 236459 421935 051205 845408 368673 790609 065161 373745 039587 430505 / 232 > 31023 [i]
- extracting embedded OOA [i] would yield OOA(31023, 206, S3, 5, 927), but