Best Known (100−34, 100, s)-Nets in Base 32
(100−34, 100, 1928)-Net over F32 — Constructive and digital
Digital (66, 100, 1928)-net over F32, using
- 321 times duplication [i] based on digital (65, 99, 1928)-net over F32, using
- net defined by OOA [i] based on linear OOA(3299, 1928, F32, 34, 34) (dual of [(1928, 34), 65453, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(3299, 32776, F32, 34) (dual of [32776, 32677, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(3297, 32768, F32, 34) (dual of [32768, 32671, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-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(33) ⊂ Ce(30) [i] based on
- OA 17-folding and stacking [i] based on linear OA(3299, 32776, F32, 34) (dual of [32776, 32677, 35]-code), using
- net defined by OOA [i] based on linear OOA(3299, 1928, F32, 34, 34) (dual of [(1928, 34), 65453, 35]-NRT-code), using
(100−34, 100, 18694)-Net over F32 — Digital
Digital (66, 100, 18694)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32100, 18694, F32, 34) (dual of [18694, 18594, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 32780, F32, 34) (dual of [32780, 32680, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- linear OA(3297, 32768, F32, 34) (dual of [32768, 32671, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(323, 12, F32, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,32) or 12-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(33) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(32100, 32780, F32, 34) (dual of [32780, 32680, 35]-code), using
(100−34, 100, large)-Net in Base 32 — Upper bound on s
There is no (66, 100, large)-net in base 32, because
- 32 times m-reduction [i] would yield (66, 68, large)-net in base 32, but