Best Known (58, 84, s)-Nets in Base 32
(58, 84, 2523)-Net over F32 — Constructive and digital
Digital (58, 84, 2523)-net over F32, using
- 321 times duplication [i] based on digital (57, 83, 2523)-net over F32, using
- net defined by OOA [i] based on linear OOA(3283, 2523, F32, 26, 26) (dual of [(2523, 26), 65515, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3283, 32799, F32, 26) (dual of [32799, 32716, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [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(3252, 32768, F32, 18) (dual of [32768, 32716, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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 Ce(25) ⊂ Ce(17) [i] based on
- OA 13-folding and stacking [i] based on linear OA(3283, 32799, F32, 26) (dual of [32799, 32716, 27]-code), using
- net defined by OOA [i] based on linear OOA(3283, 2523, F32, 26, 26) (dual of [(2523, 26), 65515, 27]-NRT-code), using
(58, 84, 5041)-Net in Base 32 — Constructive
(58, 84, 5041)-net in base 32, using
- base change [i] based on (44, 70, 5041)-net in base 64, using
- 1 times m-reduction [i] based on (44, 71, 5041)-net in base 64, using
- net defined by OOA [i] based on OOA(6471, 5041, S64, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(6471, 65534, S64, 27), using
- discarding factors based on OA(6471, 65538, S64, 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(6471, 65538, S64, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(6471, 65534, S64, 27), using
- net defined by OOA [i] based on OOA(6471, 5041, S64, 27, 27), using
- 1 times m-reduction [i] based on (44, 71, 5041)-net in base 64, using
(58, 84, 37472)-Net over F32 — Digital
Digital (58, 84, 37472)-net over F32, using
(58, 84, large)-Net in Base 32 — Upper bound on s
There is no (58, 84, large)-net in base 32, because
- 24 times m-reduction [i] would yield (58, 60, large)-net in base 32, but