Best Known (97, 97+9, s)-Nets in Base 2
(97, 97+9, 2097230)-Net over F2 — Constructive and digital
Digital (97, 106, 2097230)-net over F2, using
- net defined by OOA [i] based on linear OOA(2106, 2097230, F2, 9, 9) (dual of [(2097230, 9), 18874964, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2106, 2097230, F2, 8, 9) (dual of [(2097230, 8), 16777734, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(213, 80, F2, 8, 4) (dual of [(80, 8), 627, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(213, 80, F2, 4, 4) (dual of [(80, 4), 307, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(213, 80, F2, 3, 4) (dual of [(80, 3), 227, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (9, 13, 80)-net over F2, using
- appending kth column [i] based on linear OOA(213, 80, F2, 3, 4) (dual of [(80, 3), 227, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(213, 80, F2, 4, 4) (dual of [(80, 4), 307, 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(213, 80, F2, 8, 4) (dual of [(80, 8), 627, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2106, 2097230, F2, 8, 9) (dual of [(2097230, 8), 16777734, 10]-NRT-code), using
(97, 97+9, 2796282)-Net over F2 — Digital
Digital (97, 106, 2796282)-net over F2, using
- net defined by OOA [i] based on linear OOA(2106, 2796282, F2, 9, 9) (dual of [(2796282, 9), 25166432, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2106, 2796282, F2, 8, 9) (dual of [(2796282, 8), 22370150, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2106, 2796282, F2, 3, 9) (dual of [(2796282, 3), 8388740, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(213, 81, F2, 3, 4) (dual of [(81, 3), 230, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(213, 81, F2, 4) (dual of [81, 68, 5]-code), using
- 1 times truncation [i] based on linear OA(214, 82, F2, 5) (dual of [82, 68, 6]-code), using
- a “Sh1†code from Brouwer’s database [i]
- 1 times truncation [i] based on linear OA(214, 82, F2, 5) (dual of [82, 68, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(213, 81, F2, 4) (dual of [81, 68, 5]-code), using
- linear OOA(293, 2796201, F2, 3, 9) (dual of [(2796201, 3), 8388510, 10]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- linear OOA(213, 81, F2, 3, 4) (dual of [(81, 3), 230, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2106, 2796282, F2, 3, 9) (dual of [(2796282, 3), 8388740, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2106, 2796282, F2, 8, 9) (dual of [(2796282, 8), 22370150, 10]-NRT-code), using
(97, 97+9, large)-Net in Base 2 — Upper bound on s
There is no (97, 106, large)-net in base 2, because
- 7 times m-reduction [i] would yield (97, 99, large)-net in base 2, but