Best Known (6, 6+40, s)-Nets in Base 81
(6, 6+40, 160)-Net over F81 — Constructive and digital
Digital (6, 46, 160)-net over F81, using
- t-expansion [i] based on digital (5, 46, 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+40, 190)-Net over F81 — Digital
Digital (6, 46, 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+40, 2535)-Net in Base 81 — Upper bound on s
There is no (6, 46, 2536)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 6193 906925 594019 236179 712913 026658 502303 192500 873852 586313 351211 403081 804891 089727 193601 > 8146 [i]