Best Known (24, 50, s)-Nets in Base 81
(24, 50, 370)-Net over F81 — Constructive and digital
Digital (24, 50, 370)-net over F81, using
- t-expansion [i] based on digital (16, 50, 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
(24, 50, 955)-Net over F81 — Digital
Digital (24, 50, 955)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8150, 955, F81, 26) (dual of [955, 905, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8150, 1312, F81, 26) (dual of [1312, 1262, 27]-code), using
(24, 50, 1551105)-Net in Base 81 — Upper bound on s
There is no (24, 50, 1551106)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 265614 118830 812035 866906 029230 407157 413997 898757 514109 078416 544437 308218 661380 012346 958621 905441 > 8150 [i]