MinT - Best Known (111−31, 111, s)-Nets in Base 2

Best Known (111−31, 111, s)-Nets in Base 2

(111−31, 111, 84)-Net over F₂ — Constructive and digital

Digital (80, 111, 84)-net over F₂, using

t-expansion [i] based on digital (79, 111, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 37, 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]

(111−31, 111, 133)-Net over F₂ — Digital

Digital (80, 111, 133)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−31, 111, 1014)-Net in Base 2 — Upper bound on s

There is no (80, 111, 1015)-net in base 2, because

1 times m-reduction [i] would yield (80, 110, 1015)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1314 826028 382411 183812 605645 736388 > 2¹¹⁰ [i]