Best Known (67−34, 67, s)-Nets in Base 7
(67−34, 67, 50)-Net over F7 — Constructive and digital
Digital (33, 67, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(33,49) in PG(66,7)) for nets [i] based on digital (0, 34, 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
(67−34, 67, 105)-Net over F7 — Digital
Digital (33, 67, 105)-net over F7, using
(67−34, 67, 2550)-Net in Base 7 — Upper bound on s
There is no (33, 67, 2551)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 419 589292 887588 155005 496256 882390 768066 121640 063029 763947 > 767 [i]