Best Known (74, 74+36, s)-Nets in Base 32
(74, 74+36, 1822)-Net over F32 — Constructive and digital
Digital (74, 110, 1822)-net over F32, using
- net defined by OOA [i] based on linear OOA(32110, 1822, F32, 36, 36) (dual of [(1822, 36), 65482, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(32110, 32796, F32, 36) (dual of [32796, 32686, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [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(327, 28, F32, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- OA 18-folding and stacking [i] based on linear OA(32110, 32796, F32, 36) (dual of [32796, 32686, 37]-code), using
(74, 74+36, 29187)-Net over F32 — Digital
Digital (74, 110, 29187)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32110, 29187, F32, 36) (dual of [29187, 29077, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(32110, 32796, F32, 36) (dual of [32796, 32686, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [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(327, 28, F32, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(32110, 32796, F32, 36) (dual of [32796, 32686, 37]-code), using
(74, 74+36, large)-Net in Base 32 — Upper bound on s
There is no (74, 110, large)-net in base 32, because
- 34 times m-reduction [i] would yield (74, 76, large)-net in base 32, but