Best Known (15, 15+18, s)-Nets in Base 81
(15, 15+18, 266)-Net over F81 — Constructive and digital
Digital (15, 33, 266)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (4, 22, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- digital (2, 11, 116)-net over F81, using
(15, 15+18, 551)-Net over F81 — Digital
Digital (15, 33, 551)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8133, 551, F81, 18) (dual of [551, 518, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, 656, F81, 18) (dual of [656, 623, 19]-code), using
(15, 15+18, 515746)-Net in Base 81 — Upper bound on s
There is no (15, 33, 515747)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 955 011081 490701 508278 453684 791392 990481 898317 433430 440953 021041 > 8133 [i]