Best Known (61, 61+26, s)-Nets in Base 32
(61, 61+26, 2524)-Net over F32 — Constructive and digital
Digital (61, 87, 2524)-net over F32, using
- net defined by OOA [i] based on linear OOA(3287, 2524, F32, 26, 26) (dual of [(2524, 26), 65537, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3287, 32812, F32, 26) (dual of [32812, 32725, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(14) [i] based on
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3243, 32768, F32, 15) (dual of [32768, 32725, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3211, 44, F32, 10) (dual of [44, 33, 11]-code), using
- extended algebraic-geometric code AGe(F,33P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- construction X applied to Ce(25) ⊂ Ce(14) [i] based on
- OA 13-folding and stacking [i] based on linear OA(3287, 32812, F32, 26) (dual of [32812, 32725, 27]-code), using
(61, 61+26, 5042)-Net in Base 32 — Constructive
(61, 87, 5042)-net in base 32, using
- net defined by OOA [i] based on OOA(3287, 5042, S32, 26, 26), using
- OA 13-folding and stacking [i] based on OA(3287, 65546, S32, 26), using
- discarding factors based on OA(3287, 65547, S32, 26), using
- discarding parts of the base [i] based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- discarding factors based on OA(3287, 65547, S32, 26), using
- OA 13-folding and stacking [i] based on OA(3287, 65546, S32, 26), using
(61, 61+26, 56791)-Net over F32 — Digital
Digital (61, 87, 56791)-net over F32, using
(61, 61+26, large)-Net in Base 32 — Upper bound on s
There is no (61, 87, large)-net in base 32, because
- 24 times m-reduction [i] would yield (61, 63, large)-net in base 32, but