Best Known (6, 6+10, s)-Nets in Base 49
(6, 6+10, 101)-Net over F49 — Constructive and digital
Digital (6, 16, 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, 11, 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+10, 114)-Net over F49 — Digital
Digital (6, 16, 114)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4916, 114, F49, 2, 10) (dual of [(114, 2), 212, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(495, 50, F49, 2, 5) (dual of [(50, 2), 95, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;95,49) [i]
- linear OOA(4911, 64, F49, 2, 10) (dual of [(64, 2), 117, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,117P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(495, 50, F49, 2, 5) (dual of [(50, 2), 95, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(6, 6+10, 13904)-Net in Base 49 — Upper bound on s
There is no (6, 16, 13905)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 1104 608714 775967 756697 818609 > 4916 [i]