Best Known (55−22, 55, s)-Nets in Base 16
(55−22, 55, 531)-Net over F16 — Constructive and digital
Digital (33, 55, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 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 (22, 44, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 22, 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, 22, 257)-net over F256, using
- digital (0, 11, 17)-net over F16, using
(55−22, 55, 838)-Net over F16 — Digital
Digital (33, 55, 838)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1655, 838, F16, 22) (dual of [838, 783, 23]-code), using
- 189 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 11 times 0, 1, 27 times 0, 1, 56 times 0, 1, 88 times 0) [i] based on linear OA(1648, 642, F16, 22) (dual of [642, 594, 23]-code), using
- trace code [i] based on linear OA(25624, 321, F256, 22) (dual of [321, 297, 23]-code), using
- extended algebraic-geometric code AGe(F,298P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25624, 321, F256, 22) (dual of [321, 297, 23]-code), using
- 189 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 11 times 0, 1, 27 times 0, 1, 56 times 0, 1, 88 times 0) [i] based on linear OA(1648, 642, F16, 22) (dual of [642, 594, 23]-code), using
(55−22, 55, 343174)-Net in Base 16 — Upper bound on s
There is no (33, 55, 343175)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 685000 400795 336543 732908 840855 109496 739187 938750 606280 551157 261376 > 1655 [i]