Best Known (30−7, 30, s)-Nets in Base 64
(30−7, 30, 2804465)-Net over F64 — Constructive and digital
Digital (23, 30, 2804465)-net over F64, using
- net defined by OOA [i] based on linear OOA(6430, 2804465, F64, 9, 7) (dual of [(2804465, 9), 25240155, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(6430, 2804466, F64, 3, 7) (dual of [(2804466, 3), 8413368, 8]-NRT-code), using
- (u, u+v)-construction [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
- linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [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]
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- linear OOA(645, 8265, F64, 3, 3) (dual of [(8265, 3), 24790, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(6430, 2804466, F64, 3, 7) (dual of [(2804466, 3), 8413368, 8]-NRT-code), using
(30−7, 30, 2812585)-Net in Base 64 — Constructive
(23, 30, 2812585)-net in base 64, using
- net defined by OOA [i] based on OOA(6430, 2812585, S64, 9, 7), using
- OOA stacking with additional row [i] based on OOA(6430, 2812586, S64, 3, 7), using
- (u, u+v)-construction [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
- linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [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]
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- OOA(645, 16385, S64, 3, 3), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on OOA(6430, 2812586, S64, 3, 7), using
(30−7, 30, large)-Net over F64 — Digital
Digital (23, 30, large)-net over F64, using
- 641 times duplication [i] based on digital (22, 29, large)-net over F64, using
- t-expansion [i] based on digital (21, 29, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- t-expansion [i] based on digital (21, 29, large)-net over F64, using
(30−7, 30, large)-Net in Base 64 — Upper bound on s
There is no (23, 30, large)-net in base 64, because
- 5 times m-reduction [i] would yield (23, 25, large)-net in base 64, but