MinT - Best Known (226−44, 226, s)-Nets in Base 2

Best Known (226−44, 226, s)-Nets in Base 2

(226−44, 226, 268)-Net over F₂ — Constructive and digital

Digital (182, 226, 268)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (4, 26, 8)-net over F₂, using
  - net from sequence [i] based on digital (4, 7)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (156, 200, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 50, 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]

(226−44, 226, 625)-Net over F₂ — Digital

Digital (182, 226, 625)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−44, 226, 11168)-Net in Base 2 — Upper bound on s

There is no (182, 226, 11169)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 107 962464 100774 074963 099195 474770 032029 254396 962785 257832 666549 075728 > 2²²⁶ [i]