Best Known (103, 103+9, s)-Nets in Base 2
(103, 103+9, 2097663)-Net over F2 — Constructive and digital
Digital (103, 112, 2097663)-net over F2, using
- net defined by OOA [i] based on linear OOA(2112, 2097663, F2, 9, 9) (dual of [(2097663, 9), 18878855, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2112, 2097663, F2, 8, 9) (dual of [(2097663, 8), 16781192, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(219, 513, F2, 8, 4) (dual of [(513, 8), 4085, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(219, 513, F2, 4, 4) (dual of [(513, 4), 2033, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(219, 513, F2, 3, 4) (dual of [(513, 3), 1520, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 19, 513)-net over F2, using
- appending kth column [i] based on linear OOA(219, 513, F2, 3, 4) (dual of [(513, 3), 1520, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(219, 513, F2, 4, 4) (dual of [(513, 4), 2033, 5]-NRT-code), using
- linear OOA(293, 2097150, F2, 8, 9) (dual of [(2097150, 8), 16777107, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- linear OOA(219, 513, F2, 8, 4) (dual of [(513, 8), 4085, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2112, 2097663, F2, 8, 9) (dual of [(2097663, 8), 16781192, 10]-NRT-code), using
(103, 103+9, 4194303)-Net over F2 — Digital
Digital (103, 112, 4194303)-net over F2, using
- net defined by OOA [i] based on linear OOA(2112, 4194303, F2, 9, 9) (dual of [(4194303, 9), 37748615, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2112, 4194303, F2, 8, 9) (dual of [(4194303, 8), 33554312, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2112, 4194303, F2, 3, 9) (dual of [(4194303, 3), 12582797, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2112, 4194303, F2, 8, 9) (dual of [(4194303, 8), 33554312, 10]-NRT-code), using
(103, 103+9, large)-Net in Base 2 — Upper bound on s
There is no (103, 112, large)-net in base 2, because
- 7 times m-reduction [i] would yield (103, 105, large)-net in base 2, but