Best Known (48−16, 48, s)-Nets in Base 32
(48−16, 48, 4097)-Net over F32 — Constructive and digital
Digital (32, 48, 4097)-net over F32, using
- net defined by OOA [i] based on linear OOA(3248, 4097, F32, 16, 16) (dual of [(4097, 16), 65504, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3248, 32776, F32, 16) (dual of [32776, 32728, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3248, 32779, F32, 16) (dual of [32779, 32731, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3248, 32779, F32, 16) (dual of [32779, 32731, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3248, 32776, F32, 16) (dual of [32776, 32728, 17]-code), using
(48−16, 48, 22028)-Net over F32 — Digital
Digital (32, 48, 22028)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3248, 22028, F32, 16) (dual of [22028, 21980, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3248, 32779, F32, 16) (dual of [32779, 32731, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3248, 32779, F32, 16) (dual of [32779, 32731, 17]-code), using
(48−16, 48, large)-Net in Base 32 — Upper bound on s
There is no (32, 48, large)-net in base 32, because
- 14 times m-reduction [i] would yield (32, 34, large)-net in base 32, but