Best Known (69−35, 69, s)-Nets in Base 7
(69−35, 69, 50)-Net over F7 — Constructive and digital
Digital (34, 69, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(34,49) in PG(68,7)) for nets [i] based on digital (0, 35, 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
(69−35, 69, 107)-Net over F7 — Digital
Digital (34, 69, 107)-net over F7, using
(69−35, 69, 2861)-Net in Base 7 — Upper bound on s
There is no (34, 69, 2862)-net in base 7, because
- 1 times m-reduction [i] would yield (34, 68, 2862)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2942 698283 242181 679278 893865 757472 726240 622997 716739 419509 > 768 [i]