Best Known (80, 96, s)-Nets in Base 2
(80, 96, 512)-Net over F2 — Constructive and digital
Digital (80, 96, 512)-net over F2, using
- net defined by OOA [i] based on linear OOA(296, 512, F2, 16, 16) (dual of [(512, 16), 8096, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(296, 4096, F2, 16) (dual of [4096, 4000, 17]-code), using
- 1 times truncation [i] based on linear OA(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, 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(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(296, 4096, F2, 16) (dual of [4096, 4000, 17]-code), using
(80, 96, 1122)-Net over F2 — Digital
Digital (80, 96, 1122)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(296, 1122, F2, 3, 16) (dual of [(1122, 3), 3270, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(296, 1365, F2, 3, 16) (dual of [(1365, 3), 3999, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(296, 4095, F2, 16) (dual of [4095, 3999, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(296, 4096, F2, 16) (dual of [4096, 4000, 17]-code), using
- 1 times truncation [i] based on linear OA(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, 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(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(296, 4096, F2, 16) (dual of [4096, 4000, 17]-code), using
- OOA 3-folding [i] based on linear OA(296, 4095, F2, 16) (dual of [4095, 3999, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(296, 1365, F2, 3, 16) (dual of [(1365, 3), 3999, 17]-NRT-code), using
(80, 96, 15407)-Net in Base 2 — Upper bound on s
There is no (80, 96, 15408)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 79257 606081 110381 946934 827799 > 296 [i]