Best Known (50−7, 50, s)-Nets in Base 8
(50−7, 50, 5592401)-Net over F8 — Constructive and digital
Digital (43, 50, 5592401)-net over F8, using
- net defined by OOA [i] based on linear OOA(850, 5592401, F8, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
- OOA stacking with additional row [i] based on 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
- OOA stacking with additional row [i] based on linear OOA(850, 5592402, F8, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
(50−7, 50, large)-Net over F8 — Digital
Digital (43, 50, large)-net over F8, using
- 81 times duplication [i] based on digital (42, 49, large)-net over F8, using
(50−7, 50, large)-Net in Base 8 — Upper bound on s
There is no (43, 50, large)-net in base 8, because
- 5 times m-reduction [i] would yield (43, 45, large)-net in base 8, but