Best Known (146−26, 146, s)-Nets in Base 2
(146−26, 146, 320)-Net over F2 — Constructive and digital
Digital (120, 146, 320)-net over F2, using
- 21 times duplication [i] based on digital (119, 145, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 29, 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, 29, 64)-net over F32, using
(146−26, 146, 690)-Net over F2 — Digital
Digital (120, 146, 690)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2146, 690, F2, 2, 26) (dual of [(690, 2), 1234, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2146, 1030, F2, 2, 26) (dual of [(1030, 2), 1914, 27]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2145, 1030, F2, 2, 26) (dual of [(1030, 2), 1915, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2145, 2060, F2, 26) (dual of [2060, 1915, 27]-code), using
- strength reduction [i] based on linear OA(2145, 2060, F2, 27) (dual of [2060, 1915, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- 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(2133, 2048, F2, 25) (dual of [2048, 1915, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- strength reduction [i] based on linear OA(2145, 2060, F2, 27) (dual of [2060, 1915, 28]-code), using
- OOA 2-folding [i] based on linear OA(2145, 2060, F2, 26) (dual of [2060, 1915, 27]-code), using
- 21 times duplication [i] based on linear OOA(2145, 1030, F2, 2, 26) (dual of [(1030, 2), 1915, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2146, 1030, F2, 2, 26) (dual of [(1030, 2), 1914, 27]-NRT-code), using
(146−26, 146, 13601)-Net in Base 2 — Upper bound on s
There is no (120, 146, 13602)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 89 213717 242716 299268 755028 200368 120387 531640 > 2146 [i]