MinT - Best Known (117, 144, s)-Nets in Base 2

Best Known (117, 144, s)-Nets in Base 2

Digital (117, 144, 260)-net over F₂, using

4 times m-reduction [i] based on digital (117, 148, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 37, 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 (117, 144, 628)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁴⁴, 628, F₂, 3, 27) (dual of [(628, 3), 1740, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁴⁴, 682, F₂, 3, 27) (dual of [(682, 3), 1902, 28]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁴⁴, 2046, F₂, 27) (dual of [2046, 1902, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁴⁴, 2048, F₂, 27) (dual of [2048, 1904, 28]-code), using
      - an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

There is no (117, 144, 11589)-net in base 2, because

1 times m-reduction [i] would yield (117, 143, 11589)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 157298 511057 474115 947423 770081 148408 977104 > 2¹⁴³ [i]