Best Known (97−24, 97, s)-Nets in Base 25
(97−24, 97, 32554)-Net over F25 — Constructive and digital
Digital (73, 97, 32554)-net over F25, using
- net defined by OOA [i] based on linear OOA(2597, 32554, F25, 24, 24) (dual of [(32554, 24), 781199, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2597, 390648, F25, 24) (dual of [390648, 390551, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 390649, F25, 24) (dual of [390649, 390552, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
- linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2573, 390625, F25, 19) (dual of [390625, 390552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-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(23) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2597, 390649, F25, 24) (dual of [390649, 390552, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2597, 390648, F25, 24) (dual of [390648, 390551, 25]-code), using
(97−24, 97, 390649)-Net over F25 — Digital
Digital (73, 97, 390649)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2597, 390649, F25, 24) (dual of [390649, 390552, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
- linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2573, 390625, F25, 19) (dual of [390625, 390552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-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(23) ⊂ Ce(18) [i] based on
(97−24, 97, large)-Net in Base 25 — Upper bound on s
There is no (73, 97, large)-net in base 25, because
- 22 times m-reduction [i] would yield (73, 75, large)-net in base 25, but