Best Known (33, 33+16, s)-Nets in Base 32
(33, 33+16, 4097)-Net over F32 — Constructive and digital
Digital (33, 49, 4097)-net over F32, using
- 321 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(3248, 4097, F32, 16, 16) (dual of [(4097, 16), 65504, 17]-NRT-code), using
(33, 33+16, 28217)-Net over F32 — Digital
Digital (33, 49, 28217)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3249, 28217, F32, 16) (dual of [28217, 28168, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3249, 32783, F32, 16) (dual of [32783, 32734, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [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(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(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(3249, 32783, F32, 16) (dual of [32783, 32734, 17]-code), using
(33, 33+16, large)-Net in Base 32 — Upper bound on s
There is no (33, 49, large)-net in base 32, because
- 14 times m-reduction [i] would yield (33, 35, large)-net in base 32, but