Best Known (37−14, 37, s)-Nets in Base 16
(37−14, 37, 547)-Net over F16 — Constructive and digital
Digital (23, 37, 547)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 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 (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 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, 14, 257)-net over F256, using
- digital (2, 9, 33)-net over F16, using
(37−14, 37, 1018)-Net over F16 — Digital
Digital (23, 37, 1018)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1637, 1018, F16, 14) (dual of [1018, 981, 15]-code), using
- 495 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 45 times 0, 1, 88 times 0, 1, 140 times 0, 1, 188 times 0) [i] based on linear OA(1628, 514, F16, 14) (dual of [514, 486, 15]-code), using
- trace code [i] based on linear OA(25614, 257, F256, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using
- extended Reed–Solomon code RSe(243,256) [i]
- algebraic-geometric code AG(F,121P) 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 = 2 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 = 2 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(25614, 257, F256, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using
- 495 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 45 times 0, 1, 88 times 0, 1, 140 times 0, 1, 188 times 0) [i] based on linear OA(1628, 514, F16, 14) (dual of [514, 486, 15]-code), using
(37−14, 37, 521745)-Net in Base 16 — Upper bound on s
There is no (23, 37, 521746)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 356 814400 478288 626052 339354 436448 659941 186056 > 1637 [i]