Best Known (85−21, 85, s)-Nets in Base 32
(85−21, 85, 104859)-Net over F32 — Constructive and digital
Digital (64, 85, 104859)-net over F32, using
- 321 times duplication [i] based on digital (63, 84, 104859)-net over F32, using
- net defined by OOA [i] based on linear OOA(3284, 104859, F32, 21, 21) (dual of [(104859, 21), 2201955, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3284, 1048591, F32, 21) (dual of [1048591, 1048507, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3284, 1048596, F32, 21) (dual of [1048596, 1048512, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(3281, 1048577, F32, 21) (dual of [1048577, 1048496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3265, 1048577, F32, 17) (dual of [1048577, 1048512, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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 C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3284, 1048596, F32, 21) (dual of [1048596, 1048512, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3284, 1048591, F32, 21) (dual of [1048591, 1048507, 22]-code), using
- net defined by OOA [i] based on linear OOA(3284, 104859, F32, 21, 21) (dual of [(104859, 21), 2201955, 22]-NRT-code), using
(85−21, 85, 1048600)-Net over F32 — Digital
Digital (64, 85, 1048600)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3285, 1048600, F32, 21) (dual of [1048600, 1048515, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(20) ⊂ Ce(15) [i] based on
(85−21, 85, large)-Net in Base 32 — Upper bound on s
There is no (64, 85, large)-net in base 32, because
- 19 times m-reduction [i] would yield (64, 66, large)-net in base 32, but