MinT - Best Known (112, 112+28, s)-Nets in Base 2

Best Known (112, 112+28, s)-Nets in Base 2

Digital (112, 140, 260)-net over F₂, using

t-expansion [i] based on digital (111, 140, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 35, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

Digital (112, 140, 432)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁴⁰, 432, F₂, 2, 28) (dual of [(432, 2), 724, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁴⁰, 512, F₂, 2, 28) (dual of [(512, 2), 884, 29]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁴⁰, 1024, F₂, 28) (dual of [1024, 884, 29]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁴¹, 1025, F₂, 29) (dual of [1025, 884, 30]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]

There is no (112, 140, 6171)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 395416 423321 155720 882259 085828 481473 508836 > 2¹⁴⁰ [i]