MinT - Best Known (40, 40+21, s)-Nets in Base 2

Best Known (40, 40+21, s)-Nets in Base 2

(40, 40+21, 44)-Net over F₂ — Constructive and digital

Digital (40, 61, 44)-net over F₂, using

1 times m-reduction [i] based on digital (40, 62, 44)-net over F₂, using
- trace code for nets [i] based on digital (9, 31, 22)-net over F₄, using
  - net from sequence [i] based on digital (9, 21)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
      - an explicitly constructive algebraic function field [i]

(40, 40+21, 53)-Net over F₂ — Digital

Digital (40, 61, 53)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+21, 275)-Net in Base 2 — Upper bound on s

There is no (40, 61, 276)-net in base 2, because

1 times m-reduction [i] would yield (40, 60, 276)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 166726 868046 288154 > 2⁶⁰ [i]