Best Known (93, 93+36, s)-Nets in Base 16
(93, 93+36, 1095)-Net over F16 — Constructive and digital
Digital (93, 129, 1095)-net over F16, using
- 1 times m-reduction [i] based on digital (93, 130, 1095)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 18, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (18, 36, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 18, 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, 18, 257)-net over F256, using
- digital (39, 76, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 38, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 38, 258)-net over F256, using
- digital (6, 18, 65)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(93, 93+36, 1820)-Net in Base 16 — Constructive
(93, 129, 1820)-net in base 16, using
- net defined by OOA [i] based on OOA(16129, 1820, S16, 36, 36), using
- OA 18-folding and stacking [i] based on OA(16129, 32760, S16, 36), using
- discarding factors based on OA(16129, 32771, S16, 36), using
- discarding parts of the base [i] based on linear OA(32103, 32771, F32, 36) (dual of [32771, 32668, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- discarding parts of the base [i] based on linear OA(32103, 32771, F32, 36) (dual of [32771, 32668, 37]-code), using
- discarding factors based on OA(16129, 32771, S16, 36), using
- OA 18-folding and stacking [i] based on OA(16129, 32760, S16, 36), using
(93, 93+36, 25440)-Net over F16 — Digital
Digital (93, 129, 25440)-net over F16, using
(93, 93+36, large)-Net in Base 16 — Upper bound on s
There is no (93, 129, large)-net in base 16, because
- 34 times m-reduction [i] would yield (93, 95, large)-net in base 16, but