Best Known (47−24, 47, s)-Nets in Base 7
(47−24, 47, 50)-Net over F7 — Constructive and digital
Digital (23, 47, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(23,49) in PG(46,7)) for nets [i] based on digital (0, 24, 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
(47−24, 47, 80)-Net over F7 — Digital
Digital (23, 47, 80)-net over F7, using
(47−24, 47, 1792)-Net in Base 7 — Upper bound on s
There is no (23, 47, 1793)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 5274 306816 444354 231072 298723 858293 305377 > 747 [i]