Best Known (23−13, 23, s)-Nets in Base 81
(23−13, 23, 246)-Net over F81 — Constructive and digital
Digital (10, 23, 246)-net over F81, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 4, 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 (0, 6, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 13, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 4, 82)-net over F81, using
(23−13, 23, 398)-Net over F81 — Digital
Digital (10, 23, 398)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8123, 398, F81, 13) (dual of [398, 375, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8123, 410, F81, 13) (dual of [410, 387, 14]-code), using
(23−13, 23, 372312)-Net in Base 81 — Upper bound on s
There is no (10, 23, 372313)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 22, 372313)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 969783 189331 514417 440028 131005 776633 846241 > 8122 [i]