MinT - Best Known (123−35, 123, s)-Nets in Base 2

Best Known (123−35, 123, s)-Nets in Base 2

(123−35, 123, 84)-Net over F₂ — Constructive and digital

Digital (88, 123, 84)-net over F₂, using

t-expansion [i] based on digital (87, 123, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 41, 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]

(123−35, 123, 137)-Net over F₂ — Digital

Digital (88, 123, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−35, 123, 1013)-Net in Base 2 — Upper bound on s

There is no (88, 123, 1014)-net in base 2, because

1 times m-reduction [i] would yield (88, 122, 1014)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 363879 249346 723898 459096 480043 164497 > 2¹²² [i]