Best Known (20, 32, s)-Nets in Base 16
(20, 32, 547)-Net over F16 — Constructive and digital
Digital (20, 32, 547)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (12, 24, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
- digital (2, 8, 33)-net over F16, using
(20, 32, 1049)-Net over F16 — Digital
Digital (20, 32, 1049)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1632, 1049, F16, 12) (dual of [1049, 1017, 13]-code), using
- 527 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 39 times 0, 1, 89 times 0, 1, 154 times 0, 1, 223 times 0) [i] based on linear OA(1624, 514, F16, 12) (dual of [514, 490, 13]-code), using
- trace code [i] based on linear OA(25612, 257, F256, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using
- extended Reed–Solomon code RSe(245,256) [i]
- algebraic-geometric code AG(F,122P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- algebraic-geometric code AG(F, Q+80P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+48P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- trace code [i] based on linear OA(25612, 257, F256, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using
- 527 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 39 times 0, 1, 89 times 0, 1, 154 times 0, 1, 223 times 0) [i] based on linear OA(1624, 514, F16, 12) (dual of [514, 490, 13]-code), using
(20, 32, 527353)-Net in Base 16 — Upper bound on s
There is no (20, 32, 527354)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 340 285038 259236 646949 613301 542207 686236 > 1632 [i]