MinT - Best Known (163, 163+63, s)-Nets in Base 2

Best Known (163, 163+63, s)-Nets in Base 2

(163, 163+63, 144)-Net over F₂ — Constructive and digital

Digital (163, 226, 144)-net over F₂, using

2 times m-reduction [i] based on digital (163, 228, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 76, 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]

(163, 163+63, 236)-Net over F₂ — Digital

Digital (163, 226, 236)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+63, 1855)-Net in Base 2 — Upper bound on s

There is no (163, 226, 1856)-net in base 2, because

1 times m-reduction [i] would yield (163, 225, 1856)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 54 568790 353272 166071 175298 581890 202529 070092 336215 175065 825439 050221 > 2²²⁵ [i]