MinT - Best Known (141, 188, s)-Nets in Base 2

Best Known (141, 188, s)-Nets in Base 2

(141, 188, 195)-Net over F₂ — Constructive and digital

Digital (141, 188, 195)-net over F₂, using

t-expansion [i] based on digital (140, 188, 195)-net over F₂, using
- 1 times m-reduction [i] based on digital (140, 189, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 63, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(141, 188, 266)-Net over F₂ — Digital

Digital (141, 188, 266)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 188, 2608)-Net in Base 2 — Upper bound on s

There is no (141, 188, 2609)-net in base 2, because

1 times m-reduction [i] would yield (141, 187, 2609)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 197 238144 539530 451625 750416 272369 420839 744366 823440 736384 > 2¹⁸⁷ [i]