MinT - Best Known (207, 253, s)-Nets in Base 2

Best Known (207, 253, s)-Nets in Base 2

(207, 253, 320)-Net over F₂ — Constructive and digital

Digital (207, 253, 320)-net over F₂, using

2 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
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(207, 253, 904)-Net over F₂ — Digital

Digital (207, 253, 904)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁵³, 904, F₂, 2, 46) (dual of [(904, 2), 1555, 47]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²⁵³, 1023, F₂, 2, 46) (dual of [(1023, 2), 1793, 47]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²⁵³, 2046, F₂, 46) (dual of [2046, 1793, 47]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁵³, 2047, F₂, 46) (dual of [2047, 1794, 47]-code), using
      - 1 times truncation [i] based on linear OA(2²⁵⁴, 2048, F₂, 47) (dual of [2048, 1794, 48]-code), using
        an extension C_e(46) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,46], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]

(207, 253, 19276)-Net in Base 2 — Upper bound on s

There is no (207, 253, 19277)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14487 752292 111626 379489 106737 438382 342146 409557 856677 066345 319177 233278 055200 > 2²⁵³ [i]