Best Known (5, 5+8, s)-Nets in Base 49
(5, 5+8, 101)-Net over F49 — Constructive and digital
Digital (5, 13, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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
- digital (1, 9, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 4, 50)-net over F49, using
(5, 5+8, 148)-Net over F49 — Digital
Digital (5, 13, 148)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4913, 148, F49, 8) (dual of [148, 135, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 150, F49, 8) (dual of [150, 137, 9]-code), using
(5, 5+8, 14351)-Net in Base 49 — Upper bound on s
There is no (5, 13, 14352)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 9388 474729 647035 563009 > 4913 [i]