Best Known (72−19, 72, s)-Nets in Base 25
(72−19, 72, 1892)-Net over F25 — Constructive and digital
Digital (53, 72, 1892)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (8, 17, 156)-net over F25, using
- net defined by OOA [i] based on linear OOA(2517, 156, F25, 9, 9) (dual of [(156, 9), 1387, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2517, 625, F25, 9) (dual of [625, 608, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(2517, 625, F25, 9) (dual of [625, 608, 10]-code), using
- net defined by OOA [i] based on linear OOA(2517, 156, F25, 9, 9) (dual of [(156, 9), 1387, 10]-NRT-code), 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 (8, 17, 156)-net over F25, using
(72−19, 72, 122945)-Net over F25 — Digital
Digital (53, 72, 122945)-net over F25, using
(72−19, 72, large)-Net in Base 25 — Upper bound on s
There is no (53, 72, large)-net in base 25, because
- 17 times m-reduction [i] would yield (53, 55, large)-net in base 25, but