MinT - Best Known (38, 52, s)-Nets in Base 2

Best Known (38, 52, s)-Nets in Base 2

(38, 52, 72)-Net over F₂ — Constructive and digital

Digital (38, 52, 72)-net over F₂, using

2¹ times duplication [i] based on digital (37, 51, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 17, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(38, 52, 88)-Net over F₂ — Digital

Digital (38, 52, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 52, 572)-Net in Base 2 — Upper bound on s

There is no (38, 52, 573)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4537 941628 763528 > 2⁵² [i]