Best Known (96−28, 96, s)-Nets in Base 32
(96−28, 96, 2373)-Net over F32 — Constructive and digital
Digital (68, 96, 2373)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (54, 82, 2340)-net over F32, using
- net defined by OOA [i] based on linear OOA(3282, 2340, F32, 28, 28) (dual of [(2340, 28), 65438, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3282, 32760, F32, 28) (dual of [32760, 32678, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3282, 32760, F32, 28) (dual of [32760, 32678, 29]-code), using
- net defined by OOA [i] based on linear OOA(3282, 2340, F32, 28, 28) (dual of [(2340, 28), 65438, 29]-NRT-code), using
- digital (0, 14, 33)-net over F32, using
(96−28, 96, 4682)-Net in Base 32 — Constructive
(68, 96, 4682)-net in base 32, using
- base change [i] based on digital (32, 60, 4682)-net over F256, using
- 1 times m-reduction [i] based on digital (32, 61, 4682)-net over F256, using
- net defined by OOA [i] based on linear OOA(25661, 4682, F256, 29, 29) (dual of [(4682, 29), 135717, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25661, 65549, F256, 29) (dual of [65549, 65488, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25661, 65550, F256, 29) (dual of [65550, 65489, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(25661, 65550, F256, 29) (dual of [65550, 65489, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25661, 65549, F256, 29) (dual of [65549, 65488, 30]-code), using
- net defined by OOA [i] based on linear OOA(25661, 4682, F256, 29, 29) (dual of [(4682, 29), 135717, 30]-NRT-code), using
- 1 times m-reduction [i] based on digital (32, 61, 4682)-net over F256, using
(96−28, 96, 79207)-Net over F32 — Digital
Digital (68, 96, 79207)-net over F32, using
(96−28, 96, large)-Net in Base 32 — Upper bound on s
There is no (68, 96, large)-net in base 32, because
- 26 times m-reduction [i] would yield (68, 70, large)-net in base 32, but