Best Known (51, 51+21, s)-Nets in Base 25
(51, 51+21, 1589)-Net over F25 — Constructive and digital
Digital (51, 72, 1589)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (40, 61, 1562)-net over F25, using
- net defined by OOA [i] based on linear OOA(2561, 1562, F25, 21, 21) (dual of [(1562, 21), 32741, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2561, 15621, F25, 21) (dual of [15621, 15560, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, 15625, F25, 21) (dual of [15625, 15564, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2561, 15625, F25, 21) (dual of [15625, 15564, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2561, 15621, F25, 21) (dual of [15621, 15560, 22]-code), using
- net defined by OOA [i] based on linear OOA(2561, 1562, F25, 21, 21) (dual of [(1562, 21), 32741, 22]-NRT-code), using
- digital (1, 11, 27)-net over F25, using
(51, 51+21, 37307)-Net over F25 — Digital
Digital (51, 72, 37307)-net over F25, using
(51, 51+21, large)-Net in Base 25 — Upper bound on s
There is no (51, 72, large)-net in base 25, because
- 19 times m-reduction [i] would yield (51, 53, large)-net in base 25, but