Best Known (29−10, 29, s)-Nets in Base 32
(29−10, 29, 6555)-Net over F32 — Constructive and digital
Digital (19, 29, 6555)-net over F32, using
- net defined by OOA [i] based on linear OOA(3229, 6555, F32, 10, 10) (dual of [(6555, 10), 65521, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3229, 32775, F32, 10) (dual of [32775, 32746, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- OA 5-folding and stacking [i] based on linear OA(3229, 32775, F32, 10) (dual of [32775, 32746, 11]-code), using
(29−10, 29, 22506)-Net over F32 — Digital
Digital (19, 29, 22506)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3229, 22506, F32, 10) (dual of [22506, 22477, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3229, 32775, F32, 10) (dual of [32775, 32746, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(3229, 32775, F32, 10) (dual of [32775, 32746, 11]-code), using
(29−10, 29, large)-Net in Base 32 — Upper bound on s
There is no (19, 29, large)-net in base 32, because
- 8 times m-reduction [i] would yield (19, 21, large)-net in base 32, but