MinT - Best Known (164−43, 164, s)-Nets in Base 2

Best Known (164−43, 164, s)-Nets in Base 2

(164−43, 164, 144)-Net over F₂ — Constructive and digital

Digital (121, 164, 144)-net over F₂, using

1 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]

(164−43, 164, 211)-Net over F₂ — Digital

Digital (121, 164, 211)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−43, 164, 1853)-Net in Base 2 — Upper bound on s

There is no (121, 164, 1854)-net in base 2, because

1 times m-reduction [i] would yield (121, 163, 1854)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 805379 162395 040940 695891 657521 955638 102100 908125 > 2¹⁶³ [i]