Best Known (95, ∞, s)-Nets in Base 3
(95, ∞, 64)-Net over F3 — Constructive and digital
Digital (95, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (95, 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
(95, ∞, 96)-Net over F3 — Digital
Digital (95, m, 96)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (95, 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
(95, ∞, 203)-Net in Base 3 — Upper bound on s
There is no (95, m, 204)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (95, 1013, 204)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31013, 204, S3, 5, 918), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 674808 244296 287463 199071 551088 055120 651464 640883 325463 234253 283179 045101 205832 465753 650873 361345 363414 423404 675396 941385 628741 284229 776002 640376 899587 262887 329219 964019 256409 712533 140945 275263 133954 495950 189608 378826 084057 206279 009298 736934 101358 388370 699920 131561 202700 646260 441054 358996 917435 818286 694331 915523 083342 224868 281172 347579 872552 702703 290722 077529 381953 556209 934502 623890 341664 325866 074959 612161 499090 748291 224765 938824 821409 092614 230807 925901 724719 894072 568183 662503 335887 / 919 > 31013 [i]
- extracting embedded OOA [i] would yield OOA(31013, 204, S3, 5, 918), but