Best Known (94, 94+36, s)-Nets in Base 16
(94, 94+36, 1097)-Net over F16 — Constructive and digital
Digital (94, 130, 1097)-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 (20, 38, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 19, 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, 19, 258)-net over F256, using
- digital (38, 74, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 37, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- trace code for nets [i] based on digital (1, 37, 258)-net over F256, using
- digital (6, 18, 65)-net over F16, using
(94, 94+36, 1820)-Net in Base 16 — Constructive
(94, 130, 1820)-net in base 16, using
- base change [i] based on digital (68, 104, 1820)-net over F32, using
- 321 times duplication [i] based on digital (67, 103, 1820)-net over F32, using
- net defined by OOA [i] based on linear OOA(32103, 1820, F32, 36, 36) (dual of [(1820, 36), 65417, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(32103, 32760, F32, 36) (dual of [32760, 32657, 37]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(32103, 32760, F32, 36) (dual of [32760, 32657, 37]-code), using
- net defined by OOA [i] based on linear OOA(32103, 1820, F32, 36, 36) (dual of [(1820, 36), 65417, 37]-NRT-code), using
- 321 times duplication [i] based on digital (67, 103, 1820)-net over F32, using
(94, 94+36, 27536)-Net over F16 — Digital
Digital (94, 130, 27536)-net over F16, using
(94, 94+36, large)-Net in Base 16 — Upper bound on s
There is no (94, 130, large)-net in base 16, because
- 34 times m-reduction [i] would yield (94, 96, large)-net in base 16, but