MinT - Best Known (114, 114+37, s)-Nets in Base 2

Best Known (114, 114+37, s)-Nets in Base 2

(114, 114+37, 144)-Net over F₂ — Constructive and digital

Digital (114, 151, 144)-net over F₂, using

t-expansion [i] based on digital (113, 151, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (113, 153, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 51, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(114, 114+37, 234)-Net over F₂ — Digital

Digital (114, 151, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+37, 2409)-Net in Base 2 — Upper bound on s

There is no (114, 151, 2410)-net in base 2, because

1 times m-reduction [i] would yield (114, 150, 2410)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1429 013663 309653 747761 789880 245533 180290 717240 > 2¹⁵⁰ [i]