MinT - Best Known (60, 60+25, s)-Nets in Base 2

Best Known (60, 60+25, s)-Nets in Base 2

(60, 60+25, 72)-Net over F₂ — Constructive and digital

Digital (60, 85, 72)-net over F₂, using

2¹ times duplication [i] based on digital (59, 84, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 28, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(60, 60+25, 97)-Net over F₂ — Digital

Digital (60, 85, 97)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+25, 659)-Net in Base 2 — Upper bound on s

There is no (60, 85, 660)-net in base 2, because

1 times m-reduction [i] would yield (60, 84, 660)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19 454908 906266 174186 146868 > 2⁸⁴ [i]