Best Known (32−18, 32, s)-Nets in Base 128
(32−18, 32, 345)-Net over F128 — Constructive and digital
Digital (14, 32, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (5, 23, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (0, 9, 129)-net over F128, using
(32−18, 32, 515)-Net in Base 128 — Constructive
(14, 32, 515)-net in base 128, using
- base change [i] based on digital (10, 28, 515)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (1, 19, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (0, 9, 257)-net over F256, using
- (u, u+v)-construction [i] based on
(32−18, 32, 532)-Net over F128 — Digital
Digital (14, 32, 532)-net over F128, using
(32−18, 32, 546)-Net in Base 128
(14, 32, 546)-net in base 128, using
- base change [i] based on digital (10, 28, 546)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25628, 546, F256, 4, 18) (dual of [(546, 4), 2156, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2569, 257, F256, 4, 9) (dual of [(257, 4), 1019, 10]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1019,256) [i]
- linear OOA(25619, 289, F256, 4, 18) (dual of [(289, 4), 1137, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,1137P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- linear OOA(2569, 257, F256, 4, 9) (dual of [(257, 4), 1019, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25628, 546, F256, 4, 18) (dual of [(546, 4), 2156, 19]-NRT-code), using
(32−18, 32, 1014490)-Net in Base 128 — Upper bound on s
There is no (14, 32, 1014491)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 26 960002 435628 840351 464235 273527 238844 935711 239245 179589 343567 434154 > 12832 [i]