Best Known (19, 19+5, s)-Nets in Base 64
(19, 19+5, large)-Net over F64 — Constructive and digital
Digital (19, 24, large)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 5, large)-net over F64, using
- digital (14, 19, 4194366)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 65)-net over F64, using
- digital (12, 17, 4194301)-net over F64, using
- net defined by OOA [i] based on linear OOA(6417, 4194301, F64, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- net defined by OOA [i] based on linear OOA(6417, 4194301, F64, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(19, 19+5, large)-Net in Base 64 — Upper bound on s
There is no (19, 24, large)-net in base 64, because
- 3 times m-reduction [i] would yield (19, 21, large)-net in base 64, but