Best Known (10, 31, s)-Nets in Base 7
(10, 31, 18)-Net over F7 — Constructive and digital
Digital (10, 31, 18)-net over F7, using
- net from sequence [i] based on digital (10, 17)-sequence over F7, using
(10, 31, 38)-Net over F7 — Digital
Digital (10, 31, 38)-net over F7, using
- t-expansion [i] based on digital (9, 31, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(10, 31, 252)-Net in Base 7 — Upper bound on s
There is no (10, 31, 253)-net in base 7, because
- 1 times m-reduction [i] would yield (10, 30, 253)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 22 736091 442627 228872 544009 > 730 [i]