Best Known (45−24, 45, s)-Nets in Base 81
(45−24, 45, 370)-Net over F81 — Constructive and digital
Digital (21, 45, 370)-net over F81, using
- t-expansion [i] based on digital (16, 45, 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
(45−24, 45, 733)-Net over F81 — Digital
Digital (21, 45, 733)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8145, 733, F81, 24) (dual of [733, 688, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 820, F81, 24) (dual of [820, 775, 25]-code), using
(45−24, 45, 948609)-Net in Base 81 — Upper bound on s
There is no (21, 45, 948610)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 76 177427 537981 309969 926699 879398 461646 923509 610785 194535 796865 951117 250414 452516 617601 > 8145 [i]