Best Known (38, 38+11, s)-Nets in Base 3
(38, 38+11, 400)-Net over F3 — Constructive and digital
Digital (38, 49, 400)-net over F3, using
- 31 times duplication [i] based on digital (37, 48, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 12, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 12, 100)-net over F81, using
(38, 38+11, 719)-Net over F3 — Digital
Digital (38, 49, 719)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(349, 719, F3, 11) (dual of [719, 670, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(349, 1093, F3, 11) (dual of [1093, 1044, 12]-code), using
(38, 38+11, 49559)-Net in Base 3 — Upper bound on s
There is no (38, 49, 49560)-net in base 3, because
- 1 times m-reduction [i] would yield (38, 48, 49560)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 79766 837117 042577 348785 > 348 [i]