MinT - Best Known (71, 71+47, s)-Nets in Base 2

Best Known (71, 71+47, s)-Nets in Base 2

(71, 71+47, 56)-Net over F₂ — Constructive and digital

Digital (71, 118, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 59, 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]

(71, 71+47, 61)-Net over F₂ — Digital

Digital (71, 118, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+47, 288)-Net in Base 2 — Upper bound on s

There is no (71, 118, 289)-net in base 2, because

1 times m-reduction [i] would yield (71, 117, 289)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 178294 368360 062114 701094 850833 725952 > 2¹¹⁷ [i]