MinT - Best Known (112, 112+71, s)-Nets in Base 2

Best Known (112, 112+71, s)-Nets in Base 2

(112, 112+71, 66)-Net over F₂ — Constructive and digital

Digital (112, 183, 66)-net over F₂, using

11 times m-reduction [i] based on digital (112, 194, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 97, 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]

(112, 112+71, 92)-Net over F₂ — Digital

Digital (112, 183, 92)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+71, 461)-Net in Base 2 — Upper bound on s

There is no (112, 183, 462)-net in base 2, because

1 times m-reduction [i] would yield (112, 182, 462)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 333337 022768 247201 596639 041587 983288 681919 001169 064460 > 2¹⁸² [i]