Best Known (175, 175+36, s)-Nets in Base 2
(175, 175+36, 380)-Net over F2 — Constructive and digital
Digital (175, 211, 380)-net over F2, using
- 21 times duplication [i] based on digital (174, 210, 380)-net over F2, using
- t-expansion [i] based on digital (173, 210, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 42, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- trace code for nets [i] based on digital (5, 42, 76)-net over F32, using
- t-expansion [i] based on digital (173, 210, 380)-net over F2, using
(175, 175+36, 1014)-Net over F2 — Digital
Digital (175, 211, 1014)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2211, 1014, F2, 2, 36) (dual of [(1014, 2), 1817, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2211, 1046, F2, 2, 36) (dual of [(1046, 2), 1881, 37]-NRT-code), using
- strength reduction [i] based on linear OOA(2211, 1046, F2, 2, 37) (dual of [(1046, 2), 1881, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2211, 2092, F2, 37) (dual of [2092, 1881, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 2093, F2, 37) (dual of [2093, 1882, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(2211, 2093, F2, 37) (dual of [2093, 1882, 38]-code), using
- OOA 2-folding [i] based on linear OA(2211, 2092, F2, 37) (dual of [2092, 1881, 38]-code), using
- strength reduction [i] based on linear OOA(2211, 1046, F2, 2, 37) (dual of [(1046, 2), 1881, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2211, 1046, F2, 2, 36) (dual of [(1046, 2), 1881, 37]-NRT-code), using
(175, 175+36, 25492)-Net in Base 2 — Upper bound on s
There is no (175, 211, 25493)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3291 198273 153671 398753 020944 161836 039746 077266 737547 135715 111474 > 2211 [i]