MinT - Best Known (143, 143+57, s)-Nets in Base 2

Best Known (143, 143+57, s)-Nets in Base 2

(143, 143+57, 135)-Net over F₂ — Constructive and digital

Digital (143, 200, 135)-net over F₂, using

1 times m-reduction [i] based on digital (143, 201, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 67, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(143, 143+57, 202)-Net over F₂ — Digital

Digital (143, 200, 202)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+57, 1516)-Net in Base 2 — Upper bound on s

There is no (143, 200, 1517)-net in base 2, because

1 times m-reduction [i] would yield (143, 199, 1517)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 808651 174247 222436 271566 052756 861596 669185 128326 946169 138310 > 2¹⁹⁹ [i]