Best Known (152−16, 152, s)-Nets in Base 2
(152−16, 152, 65536)-Net over F2 — Constructive and digital
Digital (136, 152, 65536)-net over F2, using
- net defined by OOA [i] based on linear OOA(2152, 65536, F2, 16, 16) (dual of [(65536, 16), 1048424, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2152, 524288, F2, 16) (dual of [524288, 524136, 17]-code), using
- 1 times truncation [i] based on linear OA(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, 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(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(2152, 524288, F2, 16) (dual of [524288, 524136, 17]-code), using
(152−16, 152, 104857)-Net over F2 — Digital
Digital (136, 152, 104857)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, 104857, F2, 5, 16) (dual of [(104857, 5), 524133, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2152, 524285, F2, 16) (dual of [524285, 524133, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2152, 524288, F2, 16) (dual of [524288, 524136, 17]-code), using
- 1 times truncation [i] based on linear OA(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, 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(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2152, 524288, F2, 16) (dual of [524288, 524136, 17]-code), using
- OOA 5-folding [i] based on linear OA(2152, 524285, F2, 16) (dual of [524285, 524133, 17]-code), using
(152−16, 152, 1973592)-Net in Base 2 — Upper bound on s
There is no (136, 152, 1973593)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5709 005878 879544 471246 580360 139945 234985 337895 > 2152 [i]