MinT - Best Known (200, 241, s)-Nets in Base 2

Best Known (200, 241, s)-Nets in Base 2

Digital (200, 241, 490)-net over F₂, using

2¹ times duplication [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]

Digital (200, 241, 1212)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁴¹, 1212, F₂, 3, 41) (dual of [(1212, 3), 3395, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²⁴¹, 1365, F₂, 3, 41) (dual of [(1365, 3), 3854, 42]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁴¹, 4095, F₂, 41) (dual of [4095, 3854, 42]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁴¹, 4096, F₂, 41) (dual of [4096, 3855, 42]-code), using
      - an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]

There is no (200, 241, 33986)-net in base 2, because

1 times m-reduction [i] would yield (200, 240, 33986)-net in base 2, but
- 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]