Best Known (8, 8+14, s)-Nets in Base 49
(8, 8+14, 101)-Net over F49 — Constructive and digital
Digital (8, 22, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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, 15, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 7, 50)-net over F49, using
(8, 8+14, 114)-Net over F49 — Digital
Digital (8, 22, 114)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4922, 114, F49, 2, 14) (dual of [(114, 2), 206, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(497, 50, F49, 2, 7) (dual of [(50, 2), 93, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;93,49) [i]
- linear OOA(4915, 64, F49, 2, 14) (dual of [(64, 2), 113, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,113P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(497, 50, F49, 2, 7) (dual of [(50, 2), 93, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(8, 8+14, 14442)-Net in Base 49 — Upper bound on s
There is no (8, 22, 14443)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 15 294034 047606 312968 678439 954273 384049 > 4922 [i]