Best Known (36, 36+16, s)-Nets in Base 32
(36, 36+16, 4099)-Net over F32 — Constructive and digital
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
(36, 36+16, 8192)-Net in Base 32 — Constructive
(36, 52, 8192)-net in base 32, using
- 1 times m-reduction [i] based on (36, 53, 8192)-net in base 32, using
- net defined by OOA [i] based on OOA(3253, 8192, S32, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3253, 65537, S32, 17), using
- discarding factors based on OA(3253, 65538, S32, 17), using
- discarding parts of the base [i] based on linear OA(25633, 65538, F256, 17) (dual of [65538, 65505, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(25633, 65538, F256, 17) (dual of [65538, 65505, 18]-code), using
- discarding factors based on OA(3253, 65538, S32, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3253, 65537, S32, 17), using
- net defined by OOA [i] based on OOA(3253, 8192, S32, 17, 17), using
(36, 36+16, 34226)-Net over F32 — Digital
Digital (36, 52, 34226)-net over F32, using
(36, 36+16, large)-Net in Base 32 — Upper bound on s
There is no (36, 52, large)-net in base 32, because
- 14 times m-reduction [i] would yield (36, 38, large)-net in base 32, but