Best Known (27−10, 27, s)-Nets in Base 16
(27−10, 27, 634)-Net over F16 — Constructive and digital
Digital (17, 27, 634)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 120)-net over F16, using
- net defined by OOA [i] based on linear OOA(167, 120, F16, 5, 5) (dual of [(120, 5), 593, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- net defined by OOA [i] based on linear OOA(167, 120, F16, 5, 5) (dual of [(120, 5), 593, 6]-NRT-code), 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 (2, 7, 120)-net over F16, using
(27−10, 27, 1139)-Net over F16 — Digital
Digital (17, 27, 1139)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1627, 1139, F16, 10) (dual of [1139, 1112, 11]-code), using
- 556 step Varšamov–Edel lengthening with (ri) = (2, 11 times 0, 1, 72 times 0, 1, 180 times 0, 1, 289 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
- 556 step Varšamov–Edel lengthening with (ri) = (2, 11 times 0, 1, 72 times 0, 1, 180 times 0, 1, 289 times 0) [i] based on linear OA(1622, 578, F16, 10) (dual of [578, 556, 11]-code), using
(27−10, 27, 552066)-Net in Base 16 — Upper bound on s
There is no (17, 27, 552067)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 324 521269 373823 036729 147734 771776 > 1627 [i]