Best Known (81−68, 81, s)-Nets in Base 81
(81−68, 81, 224)-Net over F81 — Constructive and digital
Digital (13, 81, 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
(81−68, 81, 298)-Net over F81 — Digital
Digital (13, 81, 298)-net over F81, using
- t-expansion [i] based on digital (12, 81, 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
(81−68, 81, 5940)-Net in Base 81 — Upper bound on s
There is no (13, 81, 5941)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 38734 956350 131601 715482 192317 711485 300564 701420 357476 635072 159226 850924 449888 314194 689635 486655 735371 421244 683081 823987 662356 812892 177184 334091 010798 821921 > 8181 [i]