MinT - Best Known (113−40, 113, s)-Nets in Base 2

Best Known (113−40, 113, s)-Nets in Base 2

(113−40, 113, 66)-Net over F₂ — Constructive and digital

Digital (73, 113, 66)-net over F₂, using

3 times m-reduction [i] based on digital (73, 116, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 58, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(113−40, 113, 77)-Net over F₂ — Digital

Digital (73, 113, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−40, 113, 388)-Net in Base 2 — Upper bound on s

There is no (73, 113, 389)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10685 956888 953617 077878 381907 821064 > 2¹¹³ [i]