MinT - Best Known (241−67, 241, s)-Nets in Base 2

Best Known (241−67, 241, s)-Nets in Base 2

(241−67, 241, 144)-Net over F₂ — Constructive and digital

Digital (174, 241, 144)-net over F₂, using

t-expansion [i] based on digital (173, 241, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (173, 243, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 81, 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]

(241−67, 241, 251)-Net over F₂ — Digital

Digital (174, 241, 251)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−67, 241, 1986)-Net in Base 2 — Upper bound on s

There is no (174, 241, 1987)-net in base 2, because

1 times m-reduction [i] would yield (174, 240, 1987)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 766956 920535 839617 721602 116465 937218 402497 845145 007364 227437 319243 213800 > 2²⁴⁰ [i]