Best Known (49−17, 49, s)-Nets in Base 25
(49−17, 49, 1953)-Net over F25 — Constructive and digital
Digital (32, 49, 1953)-net over F25, using
- net defined by OOA [i] based on linear OOA(2549, 1953, F25, 17, 17) (dual of [(1953, 17), 33152, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on 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]
- OOA 8-folding and stacking with additional row [i] based on linear OA(2549, 15625, F25, 17) (dual of [15625, 15576, 18]-code), using
(49−17, 49, 7954)-Net over F25 — Digital
Digital (32, 49, 7954)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2549, 7954, F25, 17) (dual of [7954, 7905, 18]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(2549, 15625, F25, 17) (dual of [15625, 15576, 18]-code), using
(49−17, 49, large)-Net in Base 25 — Upper bound on s
There is no (32, 49, large)-net in base 25, because
- 15 times m-reduction [i] would yield (32, 34, large)-net in base 25, but