Best Known (141, 171, s)-Nets in Base 2
(141, 171, 320)-Net over F2 — Constructive and digital
Digital (141, 171, 320)-net over F2, using
- 21 times duplication [i] based on digital (140, 170, 320)-net over F2, using
- t-expansion [i] based on digital (139, 170, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 34, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- trace code for nets [i] based on digital (3, 34, 64)-net over F32, using
- t-expansion [i] based on digital (139, 170, 320)-net over F2, using
(141, 171, 798)-Net over F2 — Digital
Digital (141, 171, 798)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2171, 798, F2, 2, 30) (dual of [(798, 2), 1425, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2171, 1037, F2, 2, 30) (dual of [(1037, 2), 1903, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2171, 2074, F2, 30) (dual of [2074, 1903, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2171, 2075, F2, 30) (dual of [2075, 1904, 31]-code), using
- 1 times truncation [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 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(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2171, 2075, F2, 30) (dual of [2075, 1904, 31]-code), using
- OOA 2-folding [i] based on linear OA(2171, 2074, F2, 30) (dual of [2074, 1903, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2171, 1037, F2, 2, 30) (dual of [(1037, 2), 1903, 31]-NRT-code), using
(141, 171, 17336)-Net in Base 2 — Upper bound on s
There is no (141, 171, 17337)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2994 788784 011273 729916 373078 535498 815827 156968 342528 > 2171 [i]