Best Known (81−26, 81, s)-Nets in Base 32
(81−26, 81, 2522)-Net over F32 — Constructive and digital
Digital (55, 81, 2522)-net over F32, using
- 321 times duplication [i] based on digital (54, 80, 2522)-net over F32, using
- net defined by OOA [i] based on linear OOA(3280, 2522, F32, 26, 26) (dual of [(2522, 26), 65492, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3280, 32786, F32, 26) (dual of [32786, 32706, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3280, 32787, F32, 26) (dual of [32787, 32707, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3280, 32787, F32, 26) (dual of [32787, 32707, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3280, 32786, F32, 26) (dual of [32786, 32706, 27]-code), using
- net defined by OOA [i] based on linear OOA(3280, 2522, F32, 26, 26) (dual of [(2522, 26), 65492, 27]-NRT-code), using
(81−26, 81, 32791)-Net over F32 — Digital
Digital (55, 81, 32791)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3281, 32791, F32, 26) (dual of [32791, 32710, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [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(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(325, 23, F32, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
(81−26, 81, large)-Net in Base 32 — Upper bound on s
There is no (55, 81, large)-net in base 32, because
- 24 times m-reduction [i] would yield (55, 57, large)-net in base 32, but