MinT - Best Known (107, 107+75, s)-Nets in Base 2

Best Known (107, 107+75, s)-Nets in Base 2

(107, 107+75, 66)-Net over F₂ — Constructive and digital

Digital (107, 182, 66)-net over F₂, using

2 times m-reduction [i] based on digital (107, 184, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 92, 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]

(107, 107+75, 80)-Net over F₂ — Digital

Digital (107, 182, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+75, 383)-Net in Base 2 — Upper bound on s

There is no (107, 182, 384)-net in base 2, because

1 times m-reduction [i] would yield (107, 181, 384)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 337744 283034 910840 244891 795623 399437 810516 474684 343709 > 2¹⁸¹ [i]