Best Known (105−23, 105, s)-Nets in Base 3
(105−23, 105, 464)-Net over F3 — Constructive and digital
Digital (82, 105, 464)-net over F3, using
- 31 times duplication [i] based on digital (81, 104, 464)-net over F3, using
- t-expansion [i] based on digital (80, 104, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 26, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 26, 116)-net over F81, using
- t-expansion [i] based on digital (80, 104, 464)-net over F3, using
(105−23, 105, 982)-Net over F3 — Digital
Digital (82, 105, 982)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3105, 982, F3, 23) (dual of [982, 877, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3105, 1093, F3, 23) (dual of [1093, 988, 24]-code), using
(105−23, 105, 79596)-Net in Base 3 — Upper bound on s
There is no (82, 105, 79597)-net in base 3, because
- 1 times m-reduction [i] would yield (82, 104, 79597)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 41 751111 337001 682684 855178 987711 530412 491390 151275 > 3104 [i]