MinT - Best Known (146, 146+53, s)-Nets in Base 2

Best Known (146, 146+53, s)-Nets in Base 2

(146, 146+53, 144)-Net over F₂ — Constructive and digital

Digital (146, 199, 144)-net over F₂, using

t-expansion [i] based on digital (145, 199, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (145, 201, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 67, 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]

(146, 146+53, 237)-Net over F₂ — Digital

Digital (146, 199, 237)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+53, 2030)-Net in Base 2 — Upper bound on s

There is no (146, 199, 2031)-net in base 2, because

1 times m-reduction [i] would yield (146, 198, 2031)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 402822 202893 003104 966668 629235 584299 316560 527745 869868 052686 > 2¹⁹⁸ [i]