Best Known (39−21, 39, s)-Nets in Base 81
(39−21, 39, 370)-Net over F81 — Constructive and digital
Digital (18, 39, 370)-net over F81, using
- t-expansion [i] based on digital (16, 39, 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
(39−21, 39, 642)-Net over F81 — Digital
Digital (18, 39, 642)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8139, 642, F81, 21) (dual of [642, 603, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8139, 820, F81, 21) (dual of [820, 781, 22]-code), using
(39−21, 39, 1011876)-Net in Base 81 — Upper bound on s
There is no (18, 39, 1011877)-net in base 81, because
- 1 times m-reduction [i] would yield (18, 38, 1011877)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3 329921 014980 907418 640833 119714 004232 237277 860016 651801 789857 586665 725601 > 8138 [i]