MinT - Best Known (121, 121+41, s)-Nets in Base 2

Best Known (121, 121+41, s)-Nets in Base 2

(121, 121+41, 144)-Net over F₂ — Constructive and digital

Digital (121, 162, 144)-net over F₂, using

3 times m-reduction [i] based on digital (121, 165, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 55, 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]

(121, 121+41, 229)-Net over F₂ — Digital

Digital (121, 162, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+41, 2171)-Net in Base 2 — Upper bound on s

There is no (121, 162, 2172)-net in base 2, because

1 times m-reduction [i] would yield (121, 161, 2172)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 934565 277725 286338 520780 372443 973870 851819 681586 > 2¹⁶¹ [i]