Best Known (60, 60+27, s)-Nets in Base 32
(60, 60+27, 2523)-Net over F32 — Constructive and digital
Digital (60, 87, 2523)-net over F32, using
- 321 times duplication [i] based on digital (59, 86, 2523)-net over F32, using
- net defined by OOA [i] based on linear OOA(3286, 2523, F32, 27, 27) (dual of [(2523, 27), 68035, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3286, 32800, F32, 27) (dual of [32800, 32714, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- linear OA(3279, 32769, F32, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3255, 32769, F32, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(327, 31, F32, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(3286, 32800, F32, 27) (dual of [32800, 32714, 28]-code), using
- net defined by OOA [i] based on linear OOA(3286, 2523, F32, 27, 27) (dual of [(2523, 27), 68035, 28]-NRT-code), using
(60, 60+27, 5041)-Net in Base 32 — Constructive
(60, 87, 5041)-net in base 32, using
- 322 times duplication [i] based on (58, 85, 5041)-net in base 32, using
- net defined by OOA [i] based on OOA(3285, 5041, S32, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(3285, 65534, S32, 27), using
- discarding factors based on OA(3285, 65538, S32, 27), using
- discarding parts of the base [i] based on linear OA(25653, 65538, F256, 27) (dual of [65538, 65485, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(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(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(25653, 65538, F256, 27) (dual of [65538, 65485, 28]-code), using
- discarding factors based on OA(3285, 65538, S32, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(3285, 65534, S32, 27), using
- net defined by OOA [i] based on OOA(3285, 5041, S32, 27, 27), using
(60, 60+27, 37029)-Net over F32 — Digital
Digital (60, 87, 37029)-net over F32, using
(60, 60+27, large)-Net in Base 32 — Upper bound on s
There is no (60, 87, large)-net in base 32, because
- 25 times m-reduction [i] would yield (60, 62, large)-net in base 32, but