Best Known (53−7, 53, s)-Nets in Base 8
(53−7, 53, 5592410)-Net over F8 — Constructive and digital
Digital (46, 53, 5592410)-net over F8, using
- net defined by OOA [i] based on linear OOA(853, 5592410, F8, 9, 7) (dual of [(5592410, 9), 50331637, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(853, 5592411, F8, 3, 7) (dual of [(5592411, 3), 16777180, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(83, 9, F8, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;24,8) [i]
- linear OOA(850, 5592402, F8, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- trace code [i] based on 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
- trace code [i] based on linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- linear OOA(83, 9, F8, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(853, 5592411, F8, 3, 7) (dual of [(5592411, 3), 16777180, 8]-NRT-code), using
(53−7, 53, large)-Net over F8 — Digital
Digital (46, 53, large)-net over F8, using
- 84 times duplication [i] based on digital (42, 49, large)-net over F8, using
(53−7, 53, large)-Net in Base 8 — Upper bound on s
There is no (46, 53, large)-net in base 8, because
- 5 times m-reduction [i] would yield (46, 48, large)-net in base 8, but