Best Known (32−19, 32, s)-Nets in Base 7
(32−19, 32, 22)-Net over F7 — Constructive and digital
Digital (13, 32, 22)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (3, 22, 11)-net over F7, using
- net from sequence [i] based on digital (3, 10)-sequence over F7, using
- digital (1, 10, 13)-net over F7, using
(32−19, 32, 48)-Net over F7 — Digital
Digital (13, 32, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
(32−19, 32, 557)-Net in Base 7 — Upper bound on s
There is no (13, 32, 558)-net in base 7, because
- 1 times m-reduction [i] would yield (13, 31, 558)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 159 043810 483085 027347 884997 > 731 [i]