Best Known (20−6, 20, s)-Nets in Base 32
(20−6, 20, 11948)-Net over F32 — Constructive and digital
Digital (14, 20, 11948)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 1025)-net over F32, using
- net defined by OOA [i] based on linear OOA(324, 1025, F32, 3, 3) (dual of [(1025, 3), 3071, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(324, 1025, F32, 2, 3) (dual of [(1025, 2), 2046, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(324, 1025, F32, 3, 3) (dual of [(1025, 3), 3071, 4]-NRT-code), using
- digital (10, 16, 10923)-net over F32, using
- net defined by OOA [i] based on linear OOA(3216, 10923, F32, 6, 6) (dual of [(10923, 6), 65522, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3216, 32769, F32, 6) (dual of [32769, 32753, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 32771, F32, 6) (dual of [32771, 32755, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3213, 32768, F32, 5) (dual of [32768, 32755, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 32771, F32, 6) (dual of [32771, 32755, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(3216, 32769, F32, 6) (dual of [32769, 32753, 7]-code), using
- net defined by OOA [i] based on linear OOA(3216, 10923, F32, 6, 6) (dual of [(10923, 6), 65522, 7]-NRT-code), using
- digital (1, 4, 1025)-net over F32, using
(20−6, 20, 87382)-Net in Base 32 — Constructive
(14, 20, 87382)-net in base 32, using
- net defined by OOA [i] based on OOA(3220, 87382, S32, 6, 6), using
- OA 3-folding and stacking [i] based on OA(3220, 262146, S32, 6), using
- discarding factors based on OA(3220, 262147, S32, 6), using
- discarding parts of the base [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding parts of the base [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- discarding factors based on OA(3220, 262147, S32, 6), using
- OA 3-folding and stacking [i] based on OA(3220, 262146, S32, 6), using
(20−6, 20, 88122)-Net over F32 — Digital
Digital (14, 20, 88122)-net over F32, using
(20−6, 20, 104196)-Net in Base 32
(14, 20, 104196)-net in base 32, using
- net defined by OOA [i] based on OOA(3220, 104196, S32, 10, 6), using
- OOA 2-folding and stacking with additional row [i] based on OOA(3220, 208393, S32, 2, 6), using
- discarding factors based on OOA(3220, 208394, S32, 2, 6), using
- discarding parts of the base [i] based on linear OOA(6416, 208394, F64, 2, 6) (dual of [(208394, 2), 416772, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6416, 208394, F64, 6) (dual of [208394, 208378, 7]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6416, 208394, F64, 6) (dual of [208394, 208378, 7]-code), using
- discarding parts of the base [i] based on linear OOA(6416, 208394, F64, 2, 6) (dual of [(208394, 2), 416772, 7]-NRT-code), using
- discarding factors based on OOA(3220, 208394, S32, 2, 6), using
- OOA 2-folding and stacking with additional row [i] based on OOA(3220, 208393, S32, 2, 6), using
(20−6, 20, large)-Net in Base 32 — Upper bound on s
There is no (14, 20, large)-net in base 32, because
- 4 times m-reduction [i] would yield (14, 16, large)-net in base 32, but