Best Known (20, 20+8, s)-Nets in Base 32
(20, 20+8, 8688)-Net over F32 — Constructive and digital
Digital (20, 28, 8688)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- 1 times truncation [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- digital (14, 22, 8192)-net over F32, using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- digital (2, 6, 496)-net over F32, using
(20, 20+8, 65537)-Net in Base 32 — Constructive
(20, 28, 65537)-net in base 32, using
- net defined by OOA [i] based on OOA(3228, 65537, S32, 8, 8), using
- OA 4-folding and stacking [i] based on OA(3228, 262148, S32, 8), using
- discarding factors based on OA(3228, 262151, S32, 8), using
- discarding parts of the base [i] based on linear OA(6423, 262151, F64, 8) (dual of [262151, 262128, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(6423, 262151, F64, 8) (dual of [262151, 262128, 9]-code), using
- discarding factors based on OA(3228, 262151, S32, 8), using
- OA 4-folding and stacking [i] based on OA(3228, 262148, S32, 8), using
(20, 20+8, 114333)-Net over F32 — Digital
Digital (20, 28, 114333)-net over F32, using
(20, 20+8, large)-Net in Base 32 — Upper bound on s
There is no (20, 28, large)-net in base 32, because
- 6 times m-reduction [i] would yield (20, 22, large)-net in base 32, but