MinT - Best Known (64−20, 64, s)-Nets in Base 2

Best Known (64−20, 64, s)-Nets in Base 2

(64−20, 64, 56)-Net over F₂ — Constructive and digital

Digital (44, 64, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 32, 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]

(64−20, 64, 69)-Net over F₂ — Digital

Digital (44, 64, 69)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−20, 64, 368)-Net in Base 2 — Upper bound on s

There is no (44, 64, 369)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 18 843535 125896 928864 > 2⁶⁴ [i]