MinT - Best Known (72−24, 72, s)-Nets in Base 2

Best Known (72−24, 72, s)-Nets in Base 2

(72−24, 72, 56)-Net over F₂ — Constructive and digital

Digital (48, 72, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 36, 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]

(72−24, 72, 64)-Net over F₂ — Digital

Digital (48, 72, 64)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−24, 72, 321)-Net in Base 2 — Upper bound on s

There is no (48, 72, 322)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4826 810159 923540 709968 > 2⁷² [i]