MinT - Best Known (109−29, 109, s)-Nets in Base 2

Best Known (109−29, 109, s)-Nets in Base 2

(109−29, 109, 102)-Net over F₂ — Constructive and digital

Digital (80, 109, 102)-net over F₂, using

2¹ times duplication [i] based on digital (79, 108, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 36, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(109−29, 109, 148)-Net over F₂ — Digital

Digital (80, 109, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−29, 109, 1249)-Net in Base 2 — Upper bound on s

There is no (80, 109, 1250)-net in base 2, because

1 times m-reduction [i] would yield (80, 108, 1250)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 326 984471 861973 087979 311769 239376 > 2¹⁰⁸ [i]