MinT - Best Known (110−31, 110, s)-Nets in Base 2

Best Known (110−31, 110, s)-Nets in Base 2

(110−31, 110, 84)-Net over F₂ — Constructive and digital

Digital (79, 110, 84)-net over F₂, using

1 times m-reduction [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]

(110−31, 110, 129)-Net over F₂ — Digital

Digital (79, 110, 129)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−31, 110, 967)-Net in Base 2 — Upper bound on s

There is no (79, 110, 968)-net in base 2, because

1 times m-reduction [i] would yield (79, 109, 968)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 655 523026 702847 902316 993923 844648 > 2¹⁰⁹ [i]