Best Known (45, 45+46, s)-Nets in Base 7
(45, 45+46, 50)-Net over F7 — Constructive and digital
Digital (45, 91, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(45,49) in PG(90,7)) for nets [i] based on digital (0, 46, 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
(45, 45+46, 134)-Net over F7 — Digital
Digital (45, 91, 134)-net over F7, using
(45, 45+46, 3452)-Net in Base 7 — Upper bound on s
There is no (45, 91, 3453)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 80586 870527 171305 807754 439954 178549 833615 203842 723765 712833 254522 353474 344663 > 791 [i]