Best Known (13, 13+54, s)-Nets in Base 81
(13, 13+54, 224)-Net over F81 — Constructive and digital
Digital (13, 67, 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+54, 298)-Net over F81 — Digital
Digital (13, 67, 298)-net over F81, using
- t-expansion [i] based on digital (12, 67, 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+54, 7420)-Net in Base 81 — Upper bound on s
There is no (13, 67, 7421)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 74 127756 081463 087116 138990 785387 788824 730666 764388 638414 982798 029541 864389 858667 979108 460490 852206 955149 145812 519065 863946 787761 > 8167 [i]