Best Known (15, 15+10, s)-Nets in Base 16
(15, 15+10, 531)-Net over F16 — Constructive and digital
Digital (15, 25, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (10, 20, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 10, 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
- trace code for nets [i] based on digital (0, 10, 257)-net over F256, using
- digital (0, 5, 17)-net over F16, using
(15, 15+10, 679)-Net over F16 — Digital
Digital (15, 25, 679)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1625, 679, F16, 10) (dual of [679, 654, 11]-code), using
- 36 step Varšamov–Edel lengthening with (ri) = (1, 35 times 0) [i] based on linear OA(1624, 642, F16, 10) (dual of [642, 618, 11]-code), using
- trace code [i] based on linear OA(25612, 321, F256, 10) (dual of [321, 309, 11]-code), using
- extended algebraic-geometric code AGe(F,310P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25612, 321, F256, 10) (dual of [321, 309, 11]-code), using
- 36 step Varšamov–Edel lengthening with (ri) = (1, 35 times 0) [i] based on linear OA(1624, 642, F16, 10) (dual of [642, 618, 11]-code), using
(15, 15+10, 182112)-Net in Base 16 — Upper bound on s
There is no (15, 25, 182113)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 267674 091818 599912 463968 706976 > 1625 [i]