Best Known (6, 6+11, s)-Nets in Base 49
(6, 6+11, 101)-Net over F49 — Constructive and digital
Digital (6, 17, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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, 12, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 5, 50)-net over F49, using
(6, 6+11, 114)-Net over F49 — Digital
Digital (6, 17, 114)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4917, 114, F49, 3, 11) (dual of [(114, 3), 325, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(495, 50, F49, 3, 5) (dual of [(50, 3), 145, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;145,49) [i]
- linear OOA(4912, 64, F49, 3, 11) (dual of [(64, 3), 180, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,180P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(495, 50, F49, 3, 5) (dual of [(50, 3), 145, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(6, 6+11, 13904)-Net in Base 49 — Upper bound on s
There is no (6, 17, 13905)-net in base 49, because
- 1 times m-reduction [i] would yield (6, 16, 13905)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 1104 608714 775967 756697 818609 > 4916 [i]