Best Known (20, 26, s)-Nets in Base 64
(20, 26, 2804466)-Net over F64 — Constructive and digital
Digital (20, 26, 2804466)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 8265)-net over F64, using
- net defined by OOA [i] based on linear OOA(645, 8265, F64, 3, 3) (dual of [(8265, 3), 24790, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(645, 8265, F64, 2, 3) (dual of [(8265, 2), 16525, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(645, 8265, F64, 3, 3) (dual of [(8265, 3), 24790, 4]-NRT-code), using
- digital (15, 21, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- digital (2, 5, 8265)-net over F64, using
(20, 26, 2812586)-Net in Base 64 — Constructive
(20, 26, 2812586)-net in base 64, using
- (u, u+v)-construction [i] based on
- (2, 5, 16385)-net in base 64, using
- net defined by OOA [i] based on OOA(645, 16385, S64, 3, 3), using
- appending kth column [i] based on OOA(645, 16385, S64, 2, 3), using
- discarding parts of the base [i] based on linear OOA(1284, 16385, F128, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
- appending kth column [i] based on OOA(645, 16385, S64, 2, 3), using
- net defined by OOA [i] based on OOA(645, 16385, S64, 3, 3), using
- digital (15, 21, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- (2, 5, 16385)-net in base 64, using
(20, 26, large)-Net over F64 — Digital
Digital (20, 26, large)-net over F64, using
- 641 times duplication [i] based on digital (19, 25, large)-net over F64, using
- t-expansion [i] based on digital (18, 25, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- t-expansion [i] based on digital (18, 25, large)-net over F64, using
(20, 26, large)-Net in Base 64 — Upper bound on s
There is no (20, 26, large)-net in base 64, because
- 4 times m-reduction [i] would yield (20, 22, large)-net in base 64, but