MinT - Best Known (250−58, 250, s)-Nets in Base 2

Best Known (250−58, 250, s)-Nets in Base 2

(250−58, 250, 204)-Net over F₂ — Constructive and digital

Digital (192, 250, 204)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 34, 9)-net over F₂, using
  - net from sequence [i] based on digital (5, 8)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (158, 216, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 72, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(250−58, 250, 413)-Net over F₂ — Digital

Digital (192, 250, 413)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−58, 250, 4551)-Net in Base 2 — Upper bound on s

There is no (192, 250, 4552)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1816 513746 928377 559841 327278 188281 559536 718722 018830 159323 633342 139116 842072 > 2²⁵⁰ [i]