Best Known (13, 13+52, s)-Nets in Base 81
(13, 13+52, 224)-Net over F81 — Constructive and digital
Digital (13, 65, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(13, 13+52, 298)-Net over F81 — Digital
Digital (13, 65, 298)-net over F81, using
- t-expansion [i] based on digital (12, 65, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(13, 13+52, 7774)-Net in Base 81 — Upper bound on s
There is no (13, 65, 7775)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 11259 922883 974498 783685 434960 924554 027502 721672 474379 458808 862246 425612 049219 841057 224522 803143 896037 696487 647249 534032 172001 > 8165 [i]