MinT - Best Known (110, 110+37, s)-Nets in Base 2

Best Known (110, 110+37, s)-Nets in Base 2

(110, 110+37, 144)-Net over F₂ — Constructive and digital

Digital (110, 147, 144)-net over F₂, using

t-expansion [i] based on digital (109, 147, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 49, 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]

(110, 110+37, 214)-Net over F₂ — Digital

Digital (110, 147, 214)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+37, 2062)-Net in Base 2 — Upper bound on s

There is no (110, 147, 2063)-net in base 2, because

1 times m-reduction [i] would yield (110, 146, 2063)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 89 919489 924683 654914 765805 066057 756572 558784 > 2¹⁴⁶ [i]