Best Known (231−142, 231, s)-Nets in Base 3
(231−142, 231, 64)-Net over F3 — Constructive and digital
Digital (89, 231, 64)-net over F3, using
- net from sequence [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
(231−142, 231, 96)-Net over F3 — Digital
Digital (89, 231, 96)-net over F3, using
- net from sequence [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
(231−142, 231, 419)-Net in Base 3 — Upper bound on s
There is no (89, 231, 420)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 169 762404 457329 902535 239643 010269 074823 895906 237635 912240 156356 354300 676260 064908 109037 231680 334631 995024 979313 > 3231 [i]