MinT - Best Known (170, 170+35, s)-Nets in Base 2

Best Known (170, 170+35, s)-Nets in Base 2

Digital (170, 205, 380)-net over F₂, using

t-expansion [i] based on digital (169, 205, 380)-net over F₂, using
- trace code for nets [i] based on digital (5, 41, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

Digital (170, 205, 1092)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁰⁵, 1092, F₂, 3, 35) (dual of [(1092, 3), 3071, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²⁰⁵, 1365, F₂, 3, 35) (dual of [(1365, 3), 3890, 36]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁰⁵, 4095, F₂, 35) (dual of [4095, 3890, 36]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using
      - an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]

There is no (170, 205, 29373)-net in base 2, because

1 times m-reduction [i] would yield (170, 204, 29373)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 723580 262600 490405 094497 311764 891500 428663 100515 066805 537478 > 2²⁰⁴ [i]