Best Known (38−20, 38, s)-Nets in Base 81
(38−20, 38, 370)-Net over F81 — Constructive and digital
Digital (18, 38, 370)-net over F81, using
- t-expansion [i] based on digital (16, 38, 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
(38−20, 38, 783)-Net over F81 — Digital
Digital (18, 38, 783)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8138, 783, F81, 20) (dual of [783, 745, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8138, 1312, F81, 20) (dual of [1312, 1274, 21]-code), using
(38−20, 38, 1011876)-Net in Base 81 — Upper bound on s
There is no (18, 38, 1011877)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 329921 014980 907418 640833 119714 004232 237277 860016 651801 789857 586665 725601 > 8138 [i]