Best Known (37, 37+16, s)-Nets in Base 32
(37, 37+16, 4099)-Net over F32 — Constructive and digital
Digital (37, 53, 4099)-net over F32, using
- 321 times duplication [i] based on digital (36, 52, 4099)-net over F32, using
- net defined by OOA [i] based on linear OOA(3252, 4099, F32, 16, 16) (dual of [(4099, 16), 65532, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3252, 32792, F32, 16) (dual of [32792, 32740, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3252, 32795, F32, 16) (dual of [32795, 32743, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(8) [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(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(326, 27, F32, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(15) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3252, 32795, F32, 16) (dual of [32795, 32743, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3252, 32792, F32, 16) (dual of [32792, 32740, 17]-code), using
- net defined by OOA [i] based on linear OOA(3252, 4099, F32, 16, 16) (dual of [(4099, 16), 65532, 17]-NRT-code), using
(37, 37+16, 8193)-Net in Base 32 — Constructive
(37, 53, 8193)-net in base 32, using
- net defined by OOA [i] based on OOA(3253, 8193, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3253, 65544, S32, 16), using
- discarding parts of the base [i] based on linear OA(25633, 65544, F256, 16) (dual of [65544, 65511, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding parts of the base [i] based on linear OA(25633, 65544, F256, 16) (dual of [65544, 65511, 17]-code), using
- OA 8-folding and stacking [i] based on OA(3253, 65544, S32, 16), using
(37, 37+16, 43120)-Net over F32 — Digital
Digital (37, 53, 43120)-net over F32, using
(37, 37+16, large)-Net in Base 32 — Upper bound on s
There is no (37, 53, large)-net in base 32, because
- 14 times m-reduction [i] would yield (37, 39, large)-net in base 32, but