Best Known (38, 38+20, s)-Nets in Base 25
(38, 38+20, 1562)-Net over F25 — Constructive and digital
Digital (38, 58, 1562)-net over F25, using
- net defined by OOA [i] based on linear OOA(2558, 1562, F25, 20, 20) (dual of [(1562, 20), 31182, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2558, 15620, F25, 20) (dual of [15620, 15562, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2558, 15620, F25, 20) (dual of [15620, 15562, 21]-code), using
(38, 38+20, 8400)-Net over F25 — Digital
Digital (38, 58, 8400)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2558, 8400, F25, 20) (dual of [8400, 8342, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using
(38, 38+20, large)-Net in Base 25 — Upper bound on s
There is no (38, 58, large)-net in base 25, because
- 18 times m-reduction [i] would yield (38, 40, large)-net in base 25, but