Best Known (47, 66, s)-Nets in Base 25
(47, 66, 1764)-Net over F25 — Constructive and digital
Digital (47, 66, 1764)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- digital (36, 55, 1736)-net over F25, using
- net defined by OOA [i] based on linear OOA(2555, 1736, F25, 19, 19) (dual of [(1736, 19), 32929, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using
- net defined by OOA [i] based on linear OOA(2555, 1736, F25, 19, 19) (dual of [(1736, 19), 32929, 20]-NRT-code), using
- digital (2, 11, 28)-net over F25, using
(47, 66, 42052)-Net over F25 — Digital
Digital (47, 66, 42052)-net over F25, using
(47, 66, large)-Net in Base 25 — Upper bound on s
There is no (47, 66, large)-net in base 25, because
- 17 times m-reduction [i] would yield (47, 49, large)-net in base 25, but