Best Known (16, 16+10, s)-Nets in Base 25
(16, 16+10, 250)-Net over F25 — Constructive and digital
Digital (16, 26, 250)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- digital (9, 19, 125)-net over F25, using
- net defined by OOA [i] based on linear OOA(2519, 125, F25, 10, 10) (dual of [(125, 10), 1231, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2519, 625, F25, 10) (dual of [625, 606, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- OA 5-folding and stacking [i] based on linear OA(2519, 625, F25, 10) (dual of [625, 606, 11]-code), using
- net defined by OOA [i] based on linear OOA(2519, 125, F25, 10, 10) (dual of [(125, 10), 1231, 11]-NRT-code), using
- digital (2, 7, 300)-net over F25, using
(16, 16+10, 1893)-Net over F25 — Digital
Digital (16, 26, 1893)-net over F25, using
(16, 16+10, 2017960)-Net in Base 25 — Upper bound on s
There is no (16, 26, 2017961)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 220450 939326 562343 733792 468165 167033 > 2526 [i]