MinT - Best Known (62, 62+38, s)-Nets in Base 2

Best Known (62, 62+38, s)-Nets in Base 2

(62, 62+38, 56)-Net over F₂ — Constructive and digital

Digital (62, 100, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 50, 28)-net over F₄, using
- net from sequence [i] based on digital (12, 27)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(62, 62+38, 60)-Net over F₂ — Digital

Digital (62, 100, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+38, 277)-Net in Base 2 — Upper bound on s

There is no (62, 100, 278)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 298774 842641 555883 651204 509042 > 2¹⁰⁰ [i]