Best Known (39, 39+12, s)-Nets in Base 32
(39, 39+12, 174796)-Net over F32 — Constructive and digital
Digital (39, 51, 174796)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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 (33, 45, 174763)-net over F32, using
- net defined by OOA [i] based on linear OOA(3245, 174763, F32, 12, 12) (dual of [(174763, 12), 2097111, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3245, 1048578, F32, 12) (dual of [1048578, 1048533, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3245, 1048580, F32, 12) (dual of [1048580, 1048535, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3245, 1048580, F32, 12) (dual of [1048580, 1048535, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3245, 1048578, F32, 12) (dual of [1048578, 1048533, 13]-code), using
- net defined by OOA [i] based on linear OOA(3245, 174763, F32, 12, 12) (dual of [(174763, 12), 2097111, 13]-NRT-code), using
- digital (0, 6, 33)-net over F32, using
(39, 39+12, 349527)-Net in Base 32 — Constructive
(39, 51, 349527)-net in base 32, using
- net defined by OOA [i] based on OOA(3251, 349527, S32, 12, 12), using
- OA 6-folding and stacking [i] based on OA(3251, 2097162, S32, 12), using
- discarding factors based on OA(3251, 2097163, S32, 12), using
- discarding parts of the base [i] based on linear OA(12836, 2097163, F128, 12) (dual of [2097163, 2097127, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding parts of the base [i] based on linear OA(12836, 2097163, F128, 12) (dual of [2097163, 2097127, 13]-code), using
- discarding factors based on OA(3251, 2097163, S32, 12), using
- OA 6-folding and stacking [i] based on OA(3251, 2097162, S32, 12), using
(39, 39+12, 1506873)-Net over F32 — Digital
Digital (39, 51, 1506873)-net over F32, using
(39, 39+12, large)-Net in Base 32 — Upper bound on s
There is no (39, 51, large)-net in base 32, because
- 10 times m-reduction [i] would yield (39, 41, large)-net in base 32, but