MinT - Best Known (99, 99+22, s)-Nets in Base 2

Best Known (99, 99+22, s)-Nets in Base 2

Digital (99, 121, 260)-net over F₂, using

3 times m-reduction [i] based on digital (99, 124, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 31, 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 (99, 121, 682)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹²¹, 682, F₂, 3, 22) (dual of [(682, 3), 1925, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹²¹, 2046, F₂, 22) (dual of [2046, 1925, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹²¹, 2047, F₂, 22) (dual of [2047, 1926, 23]-code), using
    - 1 times truncation [i] based on linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using
      - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

There is no (99, 121, 10039)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 660980 407942 443395 066468 585734 282100 > 2¹²¹ [i]