Best Known (102, 102+8, s)-Nets in Base 2
(102, 102+8, 2097661)-Net over F2 — Constructive and digital
Digital (102, 110, 2097661)-net over F2, using
- net defined by OOA [i] based on linear OOA(2110, 2097661, F2, 8, 8) (dual of [(2097661, 8), 16781178, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2110, 2097661, F2, 7, 8) (dual of [(2097661, 7), 14683517, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(218, 511, F2, 7, 4) (dual of [(511, 7), 3559, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(218, 511, F2, 4, 4) (dual of [(511, 4), 2026, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(218, 511, F2, 3, 4) (dual of [(511, 3), 1515, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 18, 511)-net over F2, using
- appending kth column [i] based on linear OOA(218, 511, F2, 3, 4) (dual of [(511, 3), 1515, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(218, 511, F2, 4, 4) (dual of [(511, 4), 2026, 5]-NRT-code), using
- linear OOA(292, 2097150, F2, 7, 8) (dual of [(2097150, 7), 14679958, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(292, 8388600, F2, 8) (dual of [8388600, 8388508, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(292, 8388600, F2, 8) (dual of [8388600, 8388508, 9]-code), using
- linear OOA(218, 511, F2, 7, 4) (dual of [(511, 7), 3559, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2110, 2097661, F2, 7, 8) (dual of [(2097661, 7), 14683517, 9]-NRT-code), using
(102, 102+8, 4194812)-Net over F2 — Digital
Digital (102, 110, 4194812)-net over F2, using
- net defined by OOA [i] based on linear OOA(2110, 4194812, F2, 8, 8) (dual of [(4194812, 8), 33558386, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2110, 4194812, F2, 7, 8) (dual of [(4194812, 7), 29363574, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2110, 4194812, F2, 2, 8) (dual of [(4194812, 2), 8389514, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(218, 511, F2, 2, 4) (dual of [(511, 2), 1004, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 18, 511)-net over F2, using
- linear OOA(292, 4194301, F2, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(292, 8388602, F2, 8) (dual of [8388602, 8388510, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- OOA 2-folding [i] based on linear OA(292, 8388602, F2, 8) (dual of [8388602, 8388510, 9]-code), using
- linear OOA(218, 511, F2, 2, 4) (dual of [(511, 2), 1004, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2110, 4194812, F2, 2, 8) (dual of [(4194812, 2), 8389514, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2110, 4194812, F2, 7, 8) (dual of [(4194812, 7), 29363574, 9]-NRT-code), using
(102, 102+8, large)-Net in Base 2 — Upper bound on s
There is no (102, 110, large)-net in base 2, because
- 6 times m-reduction [i] would yield (102, 104, large)-net in base 2, but