Best Known (118, 118+16, s)-Nets in Base 2
(118, 118+16, 8196)-Net over F2 — Constructive and digital
Digital (118, 134, 8196)-net over F2, using
- net defined by OOA [i] based on linear OOA(2134, 8196, F2, 16, 16) (dual of [(8196, 16), 131002, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2134, 65568, F2, 16) (dual of [65568, 65434, 17]-code), using
- 1 times truncation [i] based on linear OA(2135, 65569, F2, 17) (dual of [65569, 65434, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2129, 65537, F2, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2135, 65569, F2, 17) (dual of [65569, 65434, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(2134, 65568, F2, 16) (dual of [65568, 65434, 17]-code), using
(118, 118+16, 16392)-Net over F2 — Digital
Digital (118, 134, 16392)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2134, 16392, F2, 4, 16) (dual of [(16392, 4), 65434, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2134, 65568, F2, 16) (dual of [65568, 65434, 17]-code), using
- 1 times truncation [i] based on linear OA(2135, 65569, F2, 17) (dual of [65569, 65434, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2129, 65537, F2, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2135, 65569, F2, 17) (dual of [65569, 65434, 18]-code), using
- OOA 4-folding [i] based on linear OA(2134, 65568, F2, 16) (dual of [65568, 65434, 17]-code), using
(118, 118+16, 414887)-Net in Base 2 — Upper bound on s
There is no (118, 134, 414888)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 21778 239374 707365 997278 391104 319265 372852 > 2134 [i]