Best Known (69−22, 69, s)-Nets in Base 25
(69−22, 69, 1422)-Net over F25 — Constructive and digital
Digital (47, 69, 1422)-net over F25, using
- 251 times duplication [i] based on digital (46, 68, 1422)-net over F25, using
- net defined by OOA [i] based on linear OOA(2568, 1422, F25, 22, 22) (dual of [(1422, 22), 31216, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2568, 15642, F25, 22) (dual of [15642, 15574, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2568, 15644, F25, 22) (dual of [15644, 15576, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2549, 15625, F25, 17) (dual of [15625, 15576, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(254, 19, F25, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(2568, 15644, F25, 22) (dual of [15644, 15576, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2568, 15642, F25, 22) (dual of [15642, 15574, 23]-code), using
- net defined by OOA [i] based on linear OOA(2568, 1422, F25, 22, 22) (dual of [(1422, 22), 31216, 23]-NRT-code), using
(69−22, 69, 15648)-Net over F25 — Digital
Digital (47, 69, 15648)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2569, 15648, F25, 22) (dual of [15648, 15579, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
(69−22, 69, large)-Net in Base 25 — Upper bound on s
There is no (47, 69, large)-net in base 25, because
- 20 times m-reduction [i] would yield (47, 49, large)-net in base 25, but