MinT - Best Known (157−39, 157, s)-Nets in Base 2

Best Known (157−39, 157, s)-Nets in Base 2

(157−39, 157, 144)-Net over F₂ — Constructive and digital

Digital (118, 157, 144)-net over F₂, using

t-expansion [i] based on digital (117, 157, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (117, 159, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 53, 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]

(157−39, 157, 234)-Net over F₂ — Digital

Digital (118, 157, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−39, 157, 2320)-Net in Base 2 — Upper bound on s

There is no (118, 157, 2321)-net in base 2, because

1 times m-reduction [i] would yield (118, 156, 2321)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91443 413681 375321 009781 754595 627348 710893 089736 > 2¹⁵⁶ [i]