Best Known (44, 59, s)-Nets in Base 32
(44, 59, 149798)-Net over F32 — Constructive and digital
Digital (44, 59, 149798)-net over F32, using
- net defined by OOA [i] based on linear OOA(3259, 149798, F32, 15, 15) (dual of [(149798, 15), 2246911, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3259, 1048587, F32, 15) (dual of [1048587, 1048528, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3259, 1048590, F32, 15) (dual of [1048590, 1048531, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(322, 14, F32, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(3259, 1048590, F32, 15) (dual of [1048590, 1048531, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3259, 1048587, F32, 15) (dual of [1048587, 1048528, 16]-code), using
(44, 59, 949131)-Net over F32 — Digital
Digital (44, 59, 949131)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3259, 949131, F32, 15) (dual of [949131, 949072, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3259, 1048590, F32, 15) (dual of [1048590, 1048531, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(322, 14, F32, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(3259, 1048590, F32, 15) (dual of [1048590, 1048531, 16]-code), using
(44, 59, large)-Net in Base 32 — Upper bound on s
There is no (44, 59, large)-net in base 32, because
- 13 times m-reduction [i] would yield (44, 46, large)-net in base 32, but