MinT - Best Known (117, 117+83, s)-Nets in Base 2

Best Known (117, 117+83, s)-Nets in Base 2

(117, 117+83, 66)-Net over F₂ — Constructive and digital

Digital (117, 200, 66)-net over F₂, using

4 times m-reduction [i] based on digital (117, 204, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 102, 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]

(117, 117+83, 85)-Net over F₂ — Digital

Digital (117, 200, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+83, 409)-Net in Base 2 — Upper bound on s

There is no (117, 200, 410)-net in base 2, because

1 times m-reduction [i] would yield (117, 199, 410)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 871953 648143 721010 798097 082837 658766 469665 007757 705103 612700 > 2¹⁹⁹ [i]