Best Known (24, 36, s)-Nets in Base 32
(24, 36, 5463)-Net over F32 — Constructive and digital
Digital (24, 36, 5463)-net over F32, using
- net defined by OOA [i] based on linear OOA(3236, 5463, F32, 12, 12) (dual of [(5463, 12), 65520, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3236, 32778, F32, 12) (dual of [32778, 32742, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 32779, F32, 12) (dual of [32779, 32743, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [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(3225, 32768, F32, 9) (dual of [32768, 32743, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 32779, F32, 12) (dual of [32779, 32743, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3236, 32778, F32, 12) (dual of [32778, 32742, 13]-code), using
(24, 36, 27075)-Net over F32 — Digital
Digital (24, 36, 27075)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3236, 27075, F32, 12) (dual of [27075, 27039, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 32779, F32, 12) (dual of [32779, 32743, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [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(3225, 32768, F32, 9) (dual of [32768, 32743, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 32779, F32, 12) (dual of [32779, 32743, 13]-code), using
(24, 36, large)-Net in Base 32 — Upper bound on s
There is no (24, 36, large)-net in base 32, because
- 10 times m-reduction [i] would yield (24, 26, large)-net in base 32, but