MinT - Best Known (54, 54+30, s)-Nets in Base 2

Best Known (54, 54+30, s)-Nets in Base 2

(54, 54+30, 56)-Net over F₂ — Constructive and digital

Digital (54, 84, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 42, 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]

(54, 54+30, 61)-Net over F₂ — Digital

Digital (54, 84, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+30, 290)-Net in Base 2 — Upper bound on s

There is no (54, 84, 291)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20 071560 213100 950659 458288 > 2⁸⁴ [i]