MinT - Best Known (200, 240, s)-Nets in Base 2

Best Known (200, 240, s)-Nets in Base 2

(200, 240, 490)-Net over F₂ — Constructive and digital

Digital (200, 240, 490)-net over F₂, using

t-expansion [i] based on digital (199, 240, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 48, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(200, 240, 1317)-Net over F₂ — Digital

Digital (200, 240, 1317)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁴⁰, 1317, F₂, 3, 40) (dual of [(1317, 3), 3711, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²⁴⁰, 1365, F₂, 3, 40) (dual of [(1365, 3), 3855, 41]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁴⁰, 4095, F₂, 40) (dual of [4095, 3855, 41]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁴⁰, 4096, F₂, 40) (dual of [4096, 3856, 41]-code), using
      - 1 times truncation [i] based on linear OA(2²⁴¹, 4097, F₂, 41) (dual of [4097, 3856, 42]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]

(200, 240, 33985)-Net in Base 2 — Upper bound on s

There is no (200, 240, 33986)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 767704 182704 783560 380109 143032 208548 417056 547010 579349 510634 822233 570384 > 2²⁴⁰ [i]