Best Known (13, 13+50, s)-Nets in Base 81
(13, 13+50, 224)-Net over F81 — Constructive and digital
Digital (13, 63, 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+50, 298)-Net over F81 — Digital
Digital (13, 63, 298)-net over F81, using
- t-expansion [i] based on digital (12, 63, 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+50, 8189)-Net in Base 81 — Upper bound on s
There is no (13, 63, 8190)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 1 717935 975270 108349 030624 635890 600259 062119 869117 847108 647393 543132 588365 345785 008536 341875 081860 850018 599222 816294 780001 > 8163 [i]