MinT - Best Known (189−79, 189, s)-Nets in Base 2

Best Known (189−79, 189, s)-Nets in Base 2

(189−79, 189, 66)-Net over F₂ — Constructive and digital

Digital (110, 189, 66)-net over F₂, using

1 times m-reduction [i] based on digital (110, 190, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 95, 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]

(189−79, 189, 80)-Net over F₂ — Digital

Digital (110, 189, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−79, 189, 380)-Net in Base 2 — Upper bound on s

There is no (110, 189, 381)-net in base 2, because

1 times m-reduction [i] would yield (110, 188, 381)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 415 959168 025527 412881 318548 761777 806905 949404 341025 699176 > 2¹⁸⁸ [i]