Best Known (144, 160, s)-Nets in Base 2
(144, 160, 131072)-Net over F2 — Constructive and digital
Digital (144, 160, 131072)-net over F2, using
- net defined by OOA [i] based on linear OOA(2160, 131072, F2, 16, 16) (dual of [(131072, 16), 2096992, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2160, 1048576, F2, 16) (dual of [1048576, 1048416, 17]-code), using
- 1 times truncation [i] based on linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(2160, 1048576, F2, 16) (dual of [1048576, 1048416, 17]-code), using
(144, 160, 209715)-Net over F2 — Digital
Digital (144, 160, 209715)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2160, 209715, F2, 5, 16) (dual of [(209715, 5), 1048415, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2160, 1048575, F2, 16) (dual of [1048575, 1048415, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 1048576, F2, 16) (dual of [1048576, 1048416, 17]-code), using
- 1 times truncation [i] based on linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 1048576, F2, 16) (dual of [1048576, 1048416, 17]-code), using
- OOA 5-folding [i] based on linear OA(2160, 1048575, F2, 16) (dual of [1048575, 1048415, 17]-code), using
(144, 160, 3947196)-Net in Base 2 — Upper bound on s
There is no (144, 160, 3947197)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 461504 024073 741482 467447 509122 735173 916055 450205 > 2160 [i]