Best Known (54, 75, s)-Nets in Base 25
(54, 75, 1628)-Net over F25 — Constructive and digital
Digital (54, 75, 1628)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-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 (4, 14, 66)-net over F25, using
(54, 75, 60456)-Net over F25 — Digital
Digital (54, 75, 60456)-net over F25, using
(54, 75, large)-Net in Base 25 — Upper bound on s
There is no (54, 75, large)-net in base 25, because
- 19 times m-reduction [i] would yield (54, 56, large)-net in base 25, but