MinT - Best Known (153−39, 153, s)-Nets in Base 2

Best Known (153−39, 153, s)-Nets in Base 2

(153−39, 153, 144)-Net over F₂ — Constructive and digital

Digital (114, 153, 144)-net over F₂, using

t-expansion [i] based on digital (113, 153, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 51, 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]

(153−39, 153, 215)-Net over F₂ — Digital

Digital (114, 153, 215)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−39, 153, 2001)-Net in Base 2 — Upper bound on s

There is no (114, 153, 2002)-net in base 2, because

1 times m-reduction [i] would yield (114, 152, 2002)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5709 798987 313924 765651 695578 651291 957783 554724 > 2¹⁵² [i]