Best Known (19−12, 19, s)-Nets in Base 49
(19−12, 19, 101)-Net over F49 — Constructive and digital
Digital (7, 19, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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, 13, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 6, 50)-net over F49, using
(19−12, 19, 114)-Net over F49 — Digital
Digital (7, 19, 114)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4919, 114, F49, 2, 12) (dual of [(114, 2), 209, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(496, 50, F49, 2, 6) (dual of [(50, 2), 94, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;94,49) [i]
- linear OOA(4913, 64, F49, 2, 12) (dual of [(64, 2), 115, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,115P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(496, 50, F49, 2, 6) (dual of [(50, 2), 94, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(19−12, 19, 14034)-Net in Base 49 — Upper bound on s
There is no (7, 19, 14035)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 129 980057 112280 783974 792573 730657 > 4919 [i]