Best Known (34, 34+18, s)-Nets in Base 25
(34, 34+18, 1736)-Net over F25 — Constructive and digital
Digital (34, 52, 1736)-net over F25, using
- net defined by OOA [i] based on linear OOA(2552, 1736, F25, 18, 18) (dual of [(1736, 18), 31196, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2552, 15624, F25, 18) (dual of [15624, 15572, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2552, 15624, F25, 18) (dual of [15624, 15572, 19]-code), using
(34, 34+18, 8088)-Net over F25 — Digital
Digital (34, 52, 8088)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2552, 8088, F25, 18) (dual of [8088, 8036, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using
(34, 34+18, large)-Net in Base 25 — Upper bound on s
There is no (34, 52, large)-net in base 25, because
- 16 times m-reduction [i] would yield (34, 36, large)-net in base 25, but