MinT - Best Known (223−50, 223, s)-Nets in Base 2

Best Known (223−50, 223, s)-Nets in Base 2

(223−50, 223, 205)-Net over F₂ — Constructive and digital

Digital (173, 223, 205)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 31, 10)-net over F₂, using
  - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (142, 192, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 64, 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]

(223−50, 223, 409)-Net over F₂ — Digital

Digital (173, 223, 409)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−50, 223, 4892)-Net in Base 2 — Upper bound on s

There is no (173, 223, 4893)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 497361 819750 657475 953513 166610 670334 403605 367504 415939 818529 620722 > 2²²³ [i]