MinT - Best Known (177−69, 177, s)-Nets in Base 2

Best Known (177−69, 177, s)-Nets in Base 2

(177−69, 177, 66)-Net over F₂ — Constructive and digital

Digital (108, 177, 66)-net over F₂, using

9 times m-reduction [i] based on digital (108, 186, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 93, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(177−69, 177, 88)-Net over F₂ — Digital

Digital (108, 177, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−69, 177, 441)-Net in Base 2 — Upper bound on s

There is no (108, 177, 442)-net in base 2, because

1 times m-reduction [i] would yield (108, 176, 442)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 100923 948266 096694 471630 568840 102871 390233 673612 347980 > 2¹⁷⁶ [i]