Best Known (23, 35, s)-Nets in Base 32
(23, 35, 5462)-Net over F32 — Constructive and digital
Digital (23, 35, 5462)-net over F32, using
- net defined by OOA [i] based on linear OOA(3235, 5462, F32, 12, 12) (dual of [(5462, 12), 65509, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3235, 32772, F32, 12) (dual of [32772, 32737, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3235, 32775, F32, 12) (dual of [32775, 32740, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] 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]
- 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(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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3235, 32775, F32, 12) (dual of [32775, 32740, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3235, 32772, F32, 12) (dual of [32772, 32737, 13]-code), using
(23, 35, 19144)-Net over F32 — Digital
Digital (23, 35, 19144)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3235, 19144, F32, 12) (dual of [19144, 19109, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3235, 32775, F32, 12) (dual of [32775, 32740, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] 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]
- 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(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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3235, 32775, F32, 12) (dual of [32775, 32740, 13]-code), using
(23, 35, large)-Net in Base 32 — Upper bound on s
There is no (23, 35, large)-net in base 32, because
- 10 times m-reduction [i] would yield (23, 25, large)-net in base 32, but