MinT - Best Known (229−63, 229, s)-Nets in Base 2

Best Known (229−63, 229, s)-Nets in Base 2

(229−63, 229, 144)-Net over F₂ — Constructive and digital

Digital (166, 229, 144)-net over F₂, using

t-expansion [i] based on digital (165, 229, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (165, 231, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 77, 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]

(229−63, 229, 246)-Net over F₂ — Digital

Digital (166, 229, 246)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−63, 229, 1987)-Net in Base 2 — Upper bound on s

There is no (166, 229, 1988)-net in base 2, because

1 times m-reduction [i] would yield (166, 228, 1988)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 437 262446 762726 136987 354502 058894 290409 435295 537251 413221 132358 743216 > 2²²⁸ [i]