Best Known (67−42, 67, s)-Nets in Base 81
(67−42, 67, 370)-Net over F81 — Constructive and digital
Digital (25, 67, 370)-net over F81, using
- t-expansion [i] based on digital (16, 67, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(67−42, 67, 392)-Net over F81 — Digital
Digital (25, 67, 392)-net over F81, using
- net from sequence [i] based on digital (25, 391)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 25 and N(F) ≥ 392, using
(67−42, 67, 133151)-Net in Base 81 — Upper bound on s
There is no (25, 67, 133152)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 73 883979 451773 309344 207795 128870 245904 475550 520091 402616 911317 534927 721586 101635 141253 470953 294008 041144 758103 199552 454114 767361 > 8167 [i]