Best Known (69, 69+5, s)-Nets in Base 5
(69, 69+5, large)-Net over F5 — Constructive and digital
Digital (69, 74, large)-net over F5, using
- 57 times duplication [i] based on digital (62, 67, large)-net over F5, using
- t-expansion [i] based on digital (61, 67, large)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (12, 15, 3050326)-net over F5, using
- net defined by OOA [i] based on linear OOA(515, 3050326, F5, 3, 3) (dual of [(3050326, 3), 9150963, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(515, 3050326, F5, 2, 3) (dual of [(3050326, 2), 6100637, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(515, 3050326, F5, 3) (dual of [3050326, 3050311, 4]-code or 3050326-cap in PG(14,5)), using
- appending kth column [i] based on linear OOA(515, 3050326, F5, 2, 3) (dual of [(3050326, 2), 6100637, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(515, 3050326, F5, 3, 3) (dual of [(3050326, 3), 9150963, 4]-NRT-code), using
- digital (46, 52, 5592402)-net over F5, using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F25, using
- digital (12, 15, 3050326)-net over F5, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (61, 67, large)-net over F5, using
(69, 69+5, large)-Net in Base 5 — Upper bound on s
There is no (69, 74, large)-net in base 5, because
- 3 times m-reduction [i] would yield (69, 71, large)-net in base 5, but