Best Known (44−10, 44, s)-Nets in Base 25
(44−10, 44, 78425)-Net over F25 — Constructive and digital
Digital (34, 44, 78425)-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 (27, 37, 78125)-net over F25, using
- net defined by OOA [i] based on linear OOA(2537, 78125, F25, 10, 10) (dual of [(78125, 10), 781213, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- OA 5-folding and stacking [i] based on linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using
- net defined by OOA [i] based on linear OOA(2537, 78125, F25, 10, 10) (dual of [(78125, 10), 781213, 11]-NRT-code), using
- digital (2, 7, 300)-net over F25, using
(44−10, 44, 1180090)-Net over F25 — Digital
Digital (34, 44, 1180090)-net over F25, using
(44−10, 44, large)-Net in Base 25 — Upper bound on s
There is no (34, 44, large)-net in base 25, because
- 8 times m-reduction [i] would yield (34, 36, large)-net in base 25, but