MinT - Best Known (64, 64+33, s)-Nets in Base 2

Best Known (64, 64+33, s)-Nets in Base 2

(64, 64+33, 66)-Net over F₂ — Constructive and digital

Digital (64, 97, 66)-net over F₂, using

1 times m-reduction [i] based on digital (64, 98, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 49, 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]

(64, 64+33, 75)-Net over F₂ — Digital

Digital (64, 97, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+33, 412)-Net in Base 2 — Upper bound on s

There is no (64, 97, 413)-net in base 2, because

1 times m-reduction [i] would yield (64, 96, 413)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 81327 730464 491833 074299 247987 > 2⁹⁶ [i]