Best Known (4, 4+7, s)-Nets in Base 49
(4, 4+7, 101)-Net over F49 — Constructive and digital
Digital (4, 11, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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, 8, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 3, 50)-net over F49, using
(4, 4+7, 129)-Net over F49 — Digital
Digital (4, 11, 129)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4911, 129, F49, 7) (dual of [129, 118, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4911, 150, F49, 7) (dual of [150, 139, 8]-code), using
(4, 4+7, 16296)-Net in Base 49 — Upper bound on s
There is no (4, 11, 16297)-net in base 49, because
- 1 times m-reduction [i] would yield (4, 10, 16297)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 79795 866765 610513 > 4910 [i]