Best Known (13, 13+34, s)-Nets in Base 81
(13, 13+34, 224)-Net over F81 — Constructive and digital
Digital (13, 47, 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+34, 298)-Net over F81 — Digital
Digital (13, 47, 298)-net over F81, using
- t-expansion [i] based on digital (12, 47, 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+34, 16945)-Net in Base 81 — Upper bound on s
There is no (13, 47, 16946)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 500242 387750 116079 963832 508448 870664 916225 794100 302676 018647 599385 801001 189949 193219 948961 > 8147 [i]