Best Known (7, 7+7, s)-Nets in Base 7
(7, 7+7, 100)-Net over F7 — Constructive and digital
Digital (7, 14, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 7, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
(7, 7+7, 1389)-Net in Base 7 — Upper bound on s
There is no (7, 14, 1390)-net in base 7, because
- 1 times m-reduction [i] would yield (7, 13, 1390)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 96995 484361 > 713 [i]