Best Known (41−21, 41, s)-Nets in Base 7
(41−21, 41, 50)-Net over F7 — Constructive and digital
Digital (20, 41, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(20,49) in PG(40,7)) for nets [i] based on digital (0, 21, 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
(41−21, 41, 72)-Net over F7 — Digital
Digital (20, 41, 72)-net over F7, using
(41−21, 41, 1806)-Net in Base 7 — Upper bound on s
There is no (20, 41, 1807)-net in base 7, because
- 1 times m-reduction [i] would yield (20, 40, 1807)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 6398 965211 121772 717569 210566 834533 > 740 [i]