Best Known (105, 105+9, s)-Nets in Base 2
(105, 105+9, 2098175)-Net over F2 — Constructive and digital
Digital (105, 114, 2098175)-net over F2, using
- 21 times duplication [i] based on digital (104, 113, 2098175)-net over F2, using
- net defined by OOA [i] based on linear OOA(2113, 2098175, F2, 9, 9) (dual of [(2098175, 9), 18883462, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2113, 2098175, F2, 8, 9) (dual of [(2098175, 8), 16785287, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(220, 1025, F2, 8, 4) (dual of [(1025, 8), 8180, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(220, 1025, F2, 4, 4) (dual of [(1025, 4), 4080, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(220, 1025, F2, 3, 4) (dual of [(1025, 3), 3055, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 20, 1025)-net over F2, using
- appending kth column [i] based on linear OOA(220, 1025, F2, 3, 4) (dual of [(1025, 3), 3055, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(220, 1025, F2, 4, 4) (dual of [(1025, 4), 4080, 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(220, 1025, F2, 8, 4) (dual of [(1025, 8), 8180, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2113, 2098175, F2, 8, 9) (dual of [(2098175, 8), 16785287, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2113, 2098175, F2, 9, 9) (dual of [(2098175, 9), 18883462, 10]-NRT-code), using
(105, 105+9, 4194303)-Net over F2 — Digital
Digital (105, 114, 4194303)-net over F2, using
- 22 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(2112, 4194303, F2, 9, 9) (dual of [(4194303, 9), 37748615, 10]-NRT-code), using
(105, 105+9, large)-Net in Base 2 — Upper bound on s
There is no (105, 114, large)-net in base 2, because
- 7 times m-reduction [i] would yield (105, 107, large)-net in base 2, but