Best Known (42−23, 42, s)-Nets in Base 7
(42−23, 42, 28)-Net over F7 — Constructive and digital
Digital (19, 42, 28)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 13)-net over F7, using
- 1 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (7, 30, 15)-net over F7, using
- net from sequence [i] based on digital (7, 14)-sequence over F7, using
- digital (1, 12, 13)-net over F7, using
(42−23, 42, 57)-Net over F7 — Digital
Digital (19, 42, 57)-net over F7, using
(42−23, 42, 1148)-Net in Base 7 — Upper bound on s
There is no (19, 42, 1149)-net in base 7, because
- 1 times m-reduction [i] would yield (19, 41, 1149)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 44699 164988 668092 265961 443803 022135 > 741 [i]