MinT - Best Known (141−41, 141, s)-Nets in Base 2

Best Known (141−41, 141, s)-Nets in Base 2

(141−41, 141, 84)-Net over F₂ — Constructive and digital

Digital (100, 141, 84)-net over F₂, using

t-expansion [i] based on digital (99, 141, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 47, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(141−41, 141, 144)-Net over F₂ — Digital

Digital (100, 141, 144)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−41, 141, 1033)-Net in Base 2 — Upper bound on s

There is no (100, 141, 1034)-net in base 2, because

1 times m-reduction [i] would yield (100, 140, 1034)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 398382 261338 269333 628266 312277 776950 041728 > 2¹⁴⁰ [i]