MinT - Best Known (62, 62+39, s)-Nets in Base 2

Best Known (62, 62+39, s)-Nets in Base 2

(62, 62+39, 54)-Net over F₂ — Constructive and digital

Digital (62, 101, 54)-net over F₂, using

3 times m-reduction [i] based on digital (62, 104, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 52, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(62, 62+39, 58)-Net over F₂ — Digital

Digital (62, 101, 58)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+39, 277)-Net in Base 2 — Upper bound on s

There is no (62, 101, 278)-net in base 2, because

1 times m-reduction [i] would yield (62, 100, 278)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 298774 842641 555883 651204 509042 > 2¹⁰⁰ [i]