MinT - Best Known (124−38, 124, s)-Nets in Base 2

Best Known (124−38, 124, s)-Nets in Base 2

(124−38, 124, 72)-Net over F₂ — Constructive and digital

Digital (86, 124, 72)-net over F₂, using

2¹ times duplication [i] based on digital (85, 123, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 41, 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]

(124−38, 124, 115)-Net over F₂ — Digital

Digital (86, 124, 115)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−38, 124, 703)-Net in Base 2 — Upper bound on s

There is no (86, 124, 704)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21 638690 426020 829244 763753 915196 394621 > 2¹²⁴ [i]