Best Known (13−7, 13, s)-Nets in Base 7
(13−7, 13, 50)-Net over F7 — Constructive and digital
Digital (6, 13, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(6,49) in PG(12,7)) 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
(13−7, 13, 725)-Net in Base 7 — Upper bound on s
There is no (6, 13, 726)-net in base 7, because
- 1 times m-reduction [i] would yield (6, 12, 726)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 13861 149193 > 712 [i]