Best Known (36, 53, s)-Nets in Base 32
(36, 53, 4098)-Net over F32 — Constructive and digital
Digital (36, 53, 4098)-net over F32, using
- net defined by OOA [i] based on linear OOA(3253, 4098, F32, 17, 17) (dual of [(4098, 17), 69613, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3253, 32785, F32, 17) (dual of [32785, 32732, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3253, 32787, F32, 17) (dual of [32787, 32734, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(3249, 32768, F32, 17) (dual of [32768, 32719, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(324, 19, F32, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(3253, 32787, F32, 17) (dual of [32787, 32734, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3253, 32785, F32, 17) (dual of [32785, 32732, 18]-code), using
(36, 53, 8192)-Net in Base 32 — Constructive
(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
(36, 53, 32787)-Net over F32 — Digital
Digital (36, 53, 32787)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3253, 32787, F32, 17) (dual of [32787, 32734, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(3249, 32768, F32, 17) (dual of [32768, 32719, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(324, 19, F32, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
(36, 53, large)-Net in Base 32 — Upper bound on s
There is no (36, 53, large)-net in base 32, because
- 15 times m-reduction [i] would yield (36, 38, large)-net in base 32, but