MinT - Best Known (190, 190+44, s)-Nets in Base 2

Best Known (190, 190+44, s)-Nets in Base 2

(190, 190+44, 274)-Net over F₂ — Constructive and digital

Digital (190, 234, 274)-net over F₂, using

2¹ times duplication [i] based on digital (189, 233, 274)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 33, 14)-net over F₂, using
    - net from sequence [i] based on digital (11, 13)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [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]

(190, 190+44, 719)-Net over F₂ — Digital

Digital (190, 234, 719)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(190, 190+44, 14379)-Net in Base 2 — Upper bound on s

There is no (190, 234, 14380)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27636 071481 532649 243633 079697 714077 681424 670900 613431 860372 759665 881956 > 2²³⁴ [i]