MinT - Best Known (243−48, 243, s)-Nets in Base 2

Best Known (243−48, 243, s)-Nets in Base 2

(243−48, 243, 267)-Net over F₂ — Constructive and digital

Digital (195, 243, 267)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 27, 7)-net over F₂, using
  - net from sequence [i] based on digital (3, 6)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (168, 216, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 54, 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]

(243−48, 243, 634)-Net over F₂ — Digital

Digital (195, 243, 634)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−48, 243, 10911)-Net in Base 2 — Upper bound on s

There is no (195, 243, 10912)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 151524 504726 198959 608615 295370 653772 856026 543057 529662 445248 210131 507007 > 2²⁴³ [i]