Best Known (108−83, 108, s)-Nets in Base 7
(108−83, 108, 31)-Net over F7 — Constructive and digital
Digital (25, 108, 31)-net over F7, using
- net from sequence [i] based on digital (25, 30)-sequence over F7, using
(108−83, 108, 72)-Net over F7 — Digital
Digital (25, 108, 72)-net over F7, using
- t-expansion [i] based on digital (22, 108, 72)-net over F7, using
- net from sequence [i] based on digital (22, 71)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 22 and N(F) ≥ 72, using
- net from sequence [i] based on digital (22, 71)-sequence over F7, using
(108−83, 108, 405)-Net in Base 7 — Upper bound on s
There is no (25, 108, 406)-net in base 7, because
- 1 times m-reduction [i] would yield (25, 107, 406)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2 803180 942869 943690 426736 075088 847231 370009 500580 101859 740319 285660 685176 005196 455743 518965 > 7107 [i]