Best Known (26−10, 26, s)-Nets in Base 16
(26−10, 26, 538)-Net over F16 — Constructive and digital
Digital (16, 26, 538)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-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 (1, 6, 24)-net over F16, using
(26−10, 26, 848)-Net over F16 — Digital
Digital (16, 26, 848)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1626, 848, F16, 10) (dual of [848, 822, 11]-code), using
- 266 step Varšamov–Edel lengthening with (ri) = (2, 11 times 0, 1, 72 times 0, 1, 180 times 0) [i] based on linear OA(1622, 578, F16, 10) (dual of [578, 556, 11]-code), using
- trace code [i] based on linear OA(25611, 289, F256, 10) (dual of [289, 278, 11]-code), using
- extended algebraic-geometric code AGe(F,278P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- trace code [i] based on linear OA(25611, 289, F256, 10) (dual of [289, 278, 11]-code), using
- 266 step Varšamov–Edel lengthening with (ri) = (2, 11 times 0, 1, 72 times 0, 1, 180 times 0) [i] based on linear OA(1622, 578, F16, 10) (dual of [578, 556, 11]-code), using
(26−10, 26, 317077)-Net in Base 16 — Upper bound on s
There is no (16, 26, 317078)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 20 282504 433454 735554 825872 606851 > 1626 [i]