Best Known (30−23, 30, s)-Nets in Base 81
(30−23, 30, 172)-Net over F81 — Constructive and digital
Digital (7, 30, 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
(30−23, 30, 190)-Net over F81 — Digital
Digital (7, 30, 190)-net over F81, using
- t-expansion [i] based on digital (6, 30, 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
(30−23, 30, 6592)-Net in Base 81 — Upper bound on s
There is no (7, 30, 6593)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 29, 6593)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 22 205905 747001 250510 264835 570221 840329 922273 102953 993841 > 8129 [i]