MinT - Best Known (161, 161+61, s)-Nets in Base 2

Best Known (161, 161+61, s)-Nets in Base 2

(161, 161+61, 144)-Net over F₂ — Constructive and digital

Digital (161, 222, 144)-net over F₂, using

3 times m-reduction [i] based on digital (161, 225, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 75, 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]

(161, 161+61, 240)-Net over F₂ — Digital

Digital (161, 222, 240)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+61, 1943)-Net in Base 2 — Upper bound on s

There is no (161, 222, 1944)-net in base 2, because

1 times m-reduction [i] would yield (161, 221, 1944)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 381864 473945 765655 440065 547090 242649 600507 120477 440944 045481 299760 > 2²²¹ [i]