Best Known (47, 47+20, s)-Nets in Base 32
(47, 47+20, 3280)-Net over F32 — Constructive and digital
Digital (47, 67, 3280)-net over F32, using
- 321 times duplication [i] based on digital (46, 66, 3280)-net over F32, using
- net defined by OOA [i] based on linear OOA(3266, 3280, F32, 20, 20) (dual of [(3280, 20), 65534, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3266, 32800, F32, 20) (dual of [32800, 32734, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, 32801, F32, 20) (dual of [32801, 32735, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(10) [i] based on
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3231, 32768, F32, 11) (dual of [32768, 32737, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(328, 33, F32, 8) (dual of [33, 25, 9]-code or 33-arc in PG(7,32)), using
- extended Reed–Solomon code RSe(25,32) [i]
- construction X applied to Ce(19) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3266, 32801, F32, 20) (dual of [32801, 32735, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3266, 32800, F32, 20) (dual of [32800, 32734, 21]-code), using
- net defined by OOA [i] based on linear OOA(3266, 3280, F32, 20, 20) (dual of [(3280, 20), 65534, 21]-NRT-code), using
(47, 47+20, 6554)-Net in Base 32 — Constructive
(47, 67, 6554)-net in base 32, using
- 1 times m-reduction [i] based on (47, 68, 6554)-net in base 32, using
- net defined by OOA [i] based on OOA(3268, 6554, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3268, 65541, S32, 21), using
- discarding factors based on OA(3268, 65542, S32, 21), using
- discarding parts of the base [i] based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- discarding parts of the base [i] based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- discarding factors based on OA(3268, 65542, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3268, 65541, S32, 21), using
- net defined by OOA [i] based on OOA(3268, 6554, S32, 21, 21), using
(47, 47+20, 51948)-Net over F32 — Digital
Digital (47, 67, 51948)-net over F32, using
(47, 47+20, large)-Net in Base 32 — Upper bound on s
There is no (47, 67, large)-net in base 32, because
- 18 times m-reduction [i] would yield (47, 49, large)-net in base 32, but