Best Known (76, 76+25, s)-Nets in Base 32
(76, 76+25, 87383)-Net over F32 — Constructive and digital
Digital (76, 101, 87383)-net over F32, using
- net defined by OOA [i] based on linear OOA(32101, 87383, F32, 25, 25) (dual of [(87383, 25), 2184474, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(32101, 1048597, F32, 25) (dual of [1048597, 1048496, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(32101, 1048600, F32, 25) (dual of [1048600, 1048499, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-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(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(32101, 1048600, F32, 25) (dual of [1048600, 1048499, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(32101, 1048597, F32, 25) (dual of [1048597, 1048496, 26]-code), using
(76, 76+25, 1048600)-Net over F32 — Digital
Digital (76, 101, 1048600)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32101, 1048600, F32, 25) (dual of [1048600, 1048499, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-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(24) ⊂ Ce(19) [i] based on
(76, 76+25, large)-Net in Base 32 — Upper bound on s
There is no (76, 101, large)-net in base 32, because
- 23 times m-reduction [i] would yield (76, 78, large)-net in base 32, but