Best Known (22, 22+10, s)-Nets in Base 25
(22, 22+10, 3128)-Net over F25 — Constructive and digital
Digital (22, 32, 3128)-net over F25, using
- 251 times duplication [i] based on digital (21, 31, 3128)-net over F25, using
- net defined by OOA [i] based on linear OOA(2531, 3128, F25, 10, 10) (dual of [(3128, 10), 31249, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2531, 15640, F25, 10) (dual of [15640, 15609, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- OA 5-folding and stacking [i] based on linear OA(2531, 15640, F25, 10) (dual of [15640, 15609, 11]-code), using
- net defined by OOA [i] based on linear OOA(2531, 3128, F25, 10, 10) (dual of [(3128, 10), 31249, 11]-NRT-code), using
(22, 22+10, 16148)-Net over F25 — Digital
Digital (22, 32, 16148)-net over F25, using
(22, 22+10, large)-Net in Base 25 — Upper bound on s
There is no (22, 32, large)-net in base 25, because
- 8 times m-reduction [i] would yield (22, 24, large)-net in base 25, but