Best Known (65, 65+32, s)-Nets in Base 25
(65, 65+32, 978)-Net over F25 — Constructive and digital
Digital (65, 97, 978)-net over F25, using
- 251 times duplication [i] based on digital (64, 96, 978)-net over F25, using
- net defined by OOA [i] based on linear OOA(2596, 978, F25, 32, 32) (dual of [(978, 32), 31200, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2596, 15648, F25, 32) (dual of [15648, 15552, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(31) ⊂ Ce(25) [i] based on
- OA 16-folding and stacking [i] based on linear OA(2596, 15648, F25, 32) (dual of [15648, 15552, 33]-code), using
- net defined by OOA [i] based on linear OOA(2596, 978, F25, 32, 32) (dual of [(978, 32), 31200, 33]-NRT-code), using
(65, 65+32, 14912)-Net over F25 — Digital
Digital (65, 97, 14912)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2597, 14912, F25, 32) (dual of [14912, 14815, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 15649, F25, 32) (dual of [15649, 15552, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2596, 15648, F25, 32) (dual of [15648, 15552, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(31) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2596, 15648, F25, 32) (dual of [15648, 15552, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 15649, F25, 32) (dual of [15649, 15552, 33]-code), using
(65, 65+32, large)-Net in Base 25 — Upper bound on s
There is no (65, 97, large)-net in base 25, because
- 30 times m-reduction [i] would yield (65, 67, large)-net in base 25, but