Best Known (115−9, 115, s)-Nets in Base 2
(115−9, 115, 2099197)-Net over F2 — Constructive and digital
Digital (106, 115, 2099197)-net over F2, using
- net defined by OOA [i] based on linear OOA(2115, 2099197, F2, 9, 9) (dual of [(2099197, 9), 18892658, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2115, 2099197, F2, 8, 9) (dual of [(2099197, 8), 16793461, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(222, 2047, F2, 8, 4) (dual of [(2047, 8), 16354, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(222, 2047, F2, 4, 4) (dual of [(2047, 4), 8166, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(222, 2047, F2, 3, 4) (dual of [(2047, 3), 6119, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (18, 22, 2047)-net over F2, using
- appending kth column [i] based on linear OOA(222, 2047, F2, 3, 4) (dual of [(2047, 3), 6119, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(222, 2047, F2, 4, 4) (dual of [(2047, 4), 8166, 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(222, 2047, F2, 8, 4) (dual of [(2047, 8), 16354, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2115, 2099197, F2, 8, 9) (dual of [(2099197, 8), 16793461, 10]-NRT-code), using
(115−9, 115, 4194304)-Net over F2 — Digital
Digital (106, 115, 4194304)-net over F2, using
- net defined by OOA [i] based on linear OOA(2115, 4194304, F2, 9, 9) (dual of [(4194304, 9), 37748621, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2115, 4194304, F2, 8, 9) (dual of [(4194304, 8), 33554317, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2115, 4194304, F2, 3, 9) (dual of [(4194304, 3), 12582797, 10]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2112, 4194303, F2, 3, 9) (dual of [(4194303, 3), 12582797, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2115, 4194304, F2, 3, 9) (dual of [(4194304, 3), 12582797, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2115, 4194304, F2, 8, 9) (dual of [(4194304, 8), 33554317, 10]-NRT-code), using
(115−9, 115, large)-Net in Base 2 — Upper bound on s
There is no (106, 115, large)-net in base 2, because
- 7 times m-reduction [i] would yield (106, 108, large)-net in base 2, but