Best Known (37, 37+12, s)-Nets in Base 3
(37, 37+12, 328)-Net over F3 — Constructive and digital
Digital (37, 49, 328)-net over F3, using
- 31 times duplication [i] based on digital (36, 48, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 12, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 12, 82)-net over F81, using
(37, 37+12, 433)-Net over F3 — Digital
Digital (37, 49, 433)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(349, 433, F3, 12) (dual of [433, 384, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(349, 728, F3, 12) (dual of [728, 679, 13]-code), using
(37, 37+12, 11789)-Net in Base 3 — Upper bound on s
There is no (37, 49, 11790)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 239411 699320 512359 725957 > 349 [i]