MinT - Best Known (53, 73, s)-Nets in Base 2

Best Known (53, 73, s)-Nets in Base 2

(53, 73, 75)-Net over F₂ — Constructive and digital

Digital (53, 73, 75)-net over F₂, using

2¹ times duplication [i] based on digital (52, 72, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 24, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]

(53, 73, 103)-Net over F₂ — Digital

Digital (53, 73, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 73, 699)-Net in Base 2 — Upper bound on s

There is no (53, 73, 700)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9538 207858 908305 016401 > 2⁷³ [i]