Best Known (15, 31, s)-Nets in Base 7
(15, 31, 50)-Net over F7 — Constructive and digital
Digital (15, 31, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(15,49) in PG(30,7)) for nets [i] based on digital (0, 16, 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
(15, 31, 60)-Net over F7 — Digital
Digital (15, 31, 60)-net over F7, using
(15, 31, 1176)-Net in Base 7 — Upper bound on s
There is no (15, 31, 1177)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 158 532868 255454 098383 324865 > 731 [i]