MinT - Best Known (240−67, 240, s)-Nets in Base 2

Best Known (240−67, 240, s)-Nets in Base 2

(240−67, 240, 144)-Net over F₂ — Constructive and digital

Digital (173, 240, 144)-net over F₂, using

3 times m-reduction [i] based on digital (173, 243, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 81, 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]

(240−67, 240, 248)-Net over F₂ — Digital

Digital (173, 240, 248)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−67, 240, 1944)-Net in Base 2 — Upper bound on s

There is no (173, 240, 1945)-net in base 2, because

1 times m-reduction [i] would yield (173, 239, 1945)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 887831 941083 728024 678726 666030 220668 544694 869770 454263 106034 462645 295000 > 2²³⁹ [i]