Best Known (41−12, 41, s)-Nets in Base 32
(41−12, 41, 5505)-Net over F32 — Constructive and digital
Digital (29, 41, 5505)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (22, 34, 5461)-net over F32, using
- net defined by OOA [i] based on linear OOA(3234, 5461, F32, 12, 12) (dual of [(5461, 12), 65498, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3234, 32766, F32, 12) (dual of [32766, 32732, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3234, 32768, F32, 12) (dual of [32768, 32734, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(3234, 32768, F32, 12) (dual of [32768, 32734, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3234, 32766, F32, 12) (dual of [32766, 32732, 13]-code), using
- net defined by OOA [i] based on linear OOA(3234, 5461, F32, 12, 12) (dual of [(5461, 12), 65498, 13]-NRT-code), using
- digital (1, 7, 44)-net over F32, using
(41−12, 41, 43691)-Net in Base 32 — Constructive
(29, 41, 43691)-net in base 32, using
- net defined by OOA [i] based on OOA(3241, 43691, S32, 12, 12), using
- OA 6-folding and stacking [i] based on OA(3241, 262146, S32, 12), using
- discarding factors based on OA(3241, 262147, S32, 12), using
- discarding parts of the base [i] based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding parts of the base [i] based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- discarding factors based on OA(3241, 262147, S32, 12), using
- OA 6-folding and stacking [i] based on OA(3241, 262146, S32, 12), using
(41−12, 41, 64535)-Net over F32 — Digital
Digital (29, 41, 64535)-net over F32, using
(41−12, 41, large)-Net in Base 32 — Upper bound on s
There is no (29, 41, large)-net in base 32, because
- 10 times m-reduction [i] would yield (29, 31, large)-net in base 32, but