Best Known (40−33, 40, s)-Nets in Base 81
(40−33, 40, 172)-Net over F81 — Constructive and digital
Digital (7, 40, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
(40−33, 40, 190)-Net over F81 — Digital
Digital (7, 40, 190)-net over F81, using
- t-expansion [i] based on digital (6, 40, 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
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(40−33, 40, 3806)-Net in Base 81 — Upper bound on s
There is no (7, 40, 3807)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 39, 3807)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 270 508321 631582 260395 607996 823136 498858 923370 377439 608658 975206 616187 656961 > 8139 [i]