Best Known (6, 6+33, s)-Nets in Base 81
(6, 6+33, 160)-Net over F81 — Constructive and digital
Digital (6, 39, 160)-net over F81, using
- t-expansion [i] based on digital (5, 39, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(6, 6+33, 190)-Net over F81 — Digital
Digital (6, 39, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(6, 6+33, 2890)-Net in Base 81 — Upper bound on s
There is no (6, 39, 2891)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 38, 2891)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3 342431 270134 749026 431048 136944 525535 087720 859052 238974 771713 709028 468481 > 8138 [i]