MinT - Best Known (107−44, 107, s)-Nets in Base 2

Best Known (107−44, 107, s)-Nets in Base 2

(107−44, 107, 44)-Net over F₂ — Constructive and digital

Digital (63, 107, 44)-net over F₂, using

1 times m-reduction [i] based on digital (63, 108, 44)-net over F₂, using
- trace code for nets [i] based on digital (9, 54, 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]

(107−44, 107, 53)-Net over F₂ — Digital

Digital (63, 107, 53)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−44, 107, 232)-Net in Base 2 — Upper bound on s

There is no (63, 107, 233)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 164 799390 848714 610600 166666 244904 > 2¹⁰⁷ [i]