Best Known (34, 34+37, s)-Nets in Base 81
(34, 34+37, 452)-Net over F81 — Constructive and digital
Digital (34, 71, 452)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 18, 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
- digital (16, 53, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- digital (0, 18, 82)-net over F81, using
(34, 34+37, 1125)-Net over F81 — Digital
Digital (34, 71, 1125)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8171, 1125, F81, 37) (dual of [1125, 1054, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(8171, 1312, F81, 37) (dual of [1312, 1241, 38]-code), using
(34, 34+37, 2494162)-Net in Base 81 — Upper bound on s
There is no (34, 71, 2494163)-net in base 81, because
- 1 times m-reduction [i] would yield (34, 70, 2494163)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 39 260251 181082 477070 655548 539632 097584 963031 499421 485582 644767 299668 039916 400898 228515 389057 301569 715374 127782 971243 477837 020912 541921 > 8170 [i]