Best Known (89−30, 89, s)-Nets in Base 32
(89−30, 89, 2185)-Net over F32 — Constructive and digital
Digital (59, 89, 2185)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 2185, F32, 30, 30) (dual of [(2185, 30), 65461, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3289, 32775, F32, 30) (dual of [32775, 32686, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(29) ⊂ Ce(27) [i] based on
- OA 15-folding and stacking [i] based on linear OA(3289, 32775, F32, 30) (dual of [32775, 32686, 31]-code), using
(89−30, 89, 19580)-Net over F32 — Digital
Digital (59, 89, 19580)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3289, 19580, F32, 30) (dual of [19580, 19491, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3289, 32775, F32, 30) (dual of [32775, 32686, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3289, 32775, F32, 30) (dual of [32775, 32686, 31]-code), using
(89−30, 89, large)-Net in Base 32 — Upper bound on s
There is no (59, 89, large)-net in base 32, because
- 28 times m-reduction [i] would yield (59, 61, large)-net in base 32, but