MinT - Best Known (193−52, 193, s)-Nets in Base 2

Best Known (193−52, 193, s)-Nets in Base 2

(193−52, 193, 144)-Net over F₂ — Constructive and digital

Digital (141, 193, 144)-net over F₂, using

2 times m-reduction [i] based on digital (141, 195, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 65, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(193−52, 193, 224)-Net over F₂ — Digital

Digital (141, 193, 224)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−52, 193, 1772)-Net in Base 2 — Upper bound on s

There is no (141, 193, 1773)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12620 387266 671640 135597 774074 900837 546795 063998 561525 146628 > 2¹⁹³ [i]