Best Known (106−26, 106, s)-Nets in Base 32
(106−26, 106, 80661)-Net over F32 — Constructive and digital
Digital (80, 106, 80661)-net over F32, using
- 322 times duplication [i] based on digital (78, 104, 80661)-net over F32, using
- net defined by OOA [i] based on linear OOA(32104, 80661, F32, 26, 26) (dual of [(80661, 26), 2097082, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(32104, 1048593, F32, 26) (dual of [1048593, 1048489, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(32104, 1048595, F32, 26) (dual of [1048595, 1048491, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(32101, 1048576, F32, 26) (dual of [1048576, 1048475, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(32104, 1048595, F32, 26) (dual of [1048595, 1048491, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(32104, 1048593, F32, 26) (dual of [1048593, 1048489, 27]-code), using
- net defined by OOA [i] based on linear OOA(32104, 80661, F32, 26, 26) (dual of [(80661, 26), 2097082, 27]-NRT-code), using
(106−26, 106, 1048605)-Net over F32 — Digital
Digital (80, 106, 1048605)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32106, 1048605, F32, 26) (dual of [1048605, 1048499, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(32101, 1048576, F32, 26) (dual of [1048576, 1048475, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(325, 29, F32, 5) (dual of [29, 24, 6]-code or 29-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
(106−26, 106, large)-Net in Base 32 — Upper bound on s
There is no (80, 106, large)-net in base 32, because
- 24 times m-reduction [i] would yield (80, 82, large)-net in base 32, but