Best Known (43, 61, s)-Nets in Base 32
(43, 61, 3674)-Net over F32 — Constructive and digital
Digital (43, 61, 3674)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (34, 52, 3641)-net over F32, using
- net defined by OOA [i] based on linear OOA(3252, 3641, F32, 18, 18) (dual of [(3641, 18), 65486, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3252, 32769, F32, 18) (dual of [32769, 32717, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3252, 32771, F32, 18) (dual of [32771, 32719, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(3252, 32768, F32, 18) (dual of [32768, 32716, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(3249, 32768, F32, 17) (dual of [32768, 32719, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3252, 32771, F32, 18) (dual of [32771, 32719, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3252, 32769, F32, 18) (dual of [32769, 32717, 19]-code), using
- net defined by OOA [i] based on linear OOA(3252, 3641, F32, 18, 18) (dual of [(3641, 18), 65486, 19]-NRT-code), using
- digital (0, 9, 33)-net over F32, using
(43, 61, 7283)-Net in Base 32 — Constructive
(43, 61, 7283)-net in base 32, using
- net defined by OOA [i] based on OOA(3261, 7283, S32, 18, 18), using
- OA 9-folding and stacking [i] based on OA(3261, 65547, S32, 18), using
- discarding parts of the base [i] based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
- OA 9-folding and stacking [i] based on OA(3261, 65547, S32, 18), using
(43, 61, 58275)-Net over F32 — Digital
Digital (43, 61, 58275)-net over F32, using
(43, 61, large)-Net in Base 32 — Upper bound on s
There is no (43, 61, large)-net in base 32, because
- 16 times m-reduction [i] would yield (43, 45, large)-net in base 32, but