Best Known (19, 39, s)-Nets in Base 7
(19, 39, 50)-Net over F7 — Constructive and digital
Digital (19, 39, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(19,49) in PG(38,7)) for nets [i] based on digital (0, 20, 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
(19, 39, 69)-Net over F7 — Digital
Digital (19, 39, 69)-net over F7, using
(19, 39, 1485)-Net in Base 7 — Upper bound on s
There is no (19, 39, 1486)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 911 796119 307045 715527 874675 527613 > 739 [i]