Best Known (254−46, 254, s)-Nets in Base 2
(254−46, 254, 320)-Net over F2 — Constructive and digital
Digital (208, 254, 320)-net over F2, using
- t-expansion [i] based on digital (207, 254, 320)-net over F2, using
- 1 times m-reduction [i] based on digital (207, 255, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 51, 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, 51, 64)-net over F32, using
- 1 times m-reduction [i] based on digital (207, 255, 320)-net over F2, using
(254−46, 254, 920)-Net over F2 — Digital
Digital (208, 254, 920)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2254, 920, F2, 2, 46) (dual of [(920, 2), 1586, 47]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2254, 1029, F2, 2, 46) (dual of [(1029, 2), 1804, 47]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2254, 2058, F2, 46) (dual of [2058, 1804, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(2254, 2059, F2, 46) (dual of [2059, 1805, 47]-code), using
- 1 times truncation [i] based on linear OA(2255, 2060, F2, 47) (dual of [2060, 1805, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(44) [i] based on
- linear OA(2254, 2048, F2, 47) (dual of [2048, 1794, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2243, 2048, F2, 45) (dual of [2048, 1805, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [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(46) ⊂ Ce(44) [i] based on
- 1 times truncation [i] based on linear OA(2255, 2060, F2, 47) (dual of [2060, 1805, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(2254, 2059, F2, 46) (dual of [2059, 1805, 47]-code), using
- OOA 2-folding [i] based on linear OA(2254, 2058, F2, 46) (dual of [2058, 1804, 47]-code), using
- discarding factors / shortening the dual code based on linear OOA(2254, 1029, F2, 2, 46) (dual of [(1029, 2), 1804, 47]-NRT-code), using
(254−46, 254, 19867)-Net in Base 2 — Upper bound on s
There is no (208, 254, 19868)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 28981 233994 029505 846333 528344 496381 097992 457210 367014 131481 748321 913711 366386 > 2254 [i]