MinT - Best Known (202, 202+47, s)-Nets in Base 2

Best Known (202, 202+47, s)-Nets in Base 2

(202, 202+47, 275)-Net over F₂ — Constructive and digital

Digital (202, 249, 275)-net over F₂, using

2¹ times duplication [i] based on digital (201, 248, 275)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 36, 15)-net over F₂, using
    - net from sequence [i] based on digital (13, 14)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 13 and N(F) ≥ 15, using
        an explicitly constructive algebraic function field [i]
  2. digital (165, 212, 260)-net over F₂, using
    - trace code for nets [i] based on digital (6, 53, 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]

(202, 202+47, 747)-Net over F₂ — Digital

Digital (202, 249, 747)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202, 202+47, 16575)-Net in Base 2 — Upper bound on s

There is no (202, 249, 16576)-net in base 2, because

1 times m-reduction [i] would yield (202, 248, 16576)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 452 885091 665701 166923 120095 804969 718123 740312 912933 335267 576836 366385 996173 > 2²⁴⁸ [i]