MinT - Best Known (113−39, 113, s)-Nets in Base 2

Best Known (113−39, 113, s)-Nets in Base 2

(113−39, 113, 66)-Net over F₂ — Constructive and digital

Digital (74, 113, 66)-net over F₂, using

5 times m-reduction [i] based on digital (74, 118, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 59, 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]

(113−39, 113, 81)-Net over F₂ — Digital

Digital (74, 113, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−39, 113, 444)-Net in Base 2 — Upper bound on s

There is no (74, 113, 445)-net in base 2, because

1 times m-reduction [i] would yield (74, 112, 445)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5302 739132 624937 787172 965734 658048 > 2¹¹² [i]