Best Known (21−12, 21, s)-Nets in Base 81
(21−12, 21, 216)-Net over F81 — Constructive and digital
Digital (9, 21, 216)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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
- digital (2, 14, 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 (1, 7, 100)-net over F81, using
(21−12, 21, 367)-Net over F81 — Digital
Digital (9, 21, 367)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8121, 367, F81, 12) (dual of [367, 346, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8121, 410, F81, 12) (dual of [410, 389, 13]-code), using
(21−12, 21, 178987)-Net in Base 81 — Upper bound on s
There is no (9, 21, 178988)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 11972 598109 702689 869691 697917 031813 850241 > 8121 [i]