Best Known (13, 78, s)-Nets in Base 81
(13, 78, 224)-Net over F81 — Constructive and digital
Digital (13, 78, 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, 78, 298)-Net over F81 — Digital
Digital (13, 78, 298)-net over F81, using
- t-expansion [i] based on digital (12, 78, 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, 78, 6237)-Net in Base 81 — Upper bound on s
There is no (13, 78, 6238)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 77, 6238)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 902 651912 004120 834529 047997 632125 790094 671854 161413 255013 382486 195390 063026 749559 845807 504068 033461 800595 191116 374385 718735 671274 431803 330849 479681 > 8177 [i]