MinT - Best Known (119, 119+39, s)-Nets in Base 2

Best Known (119, 119+39, s)-Nets in Base 2

(119, 119+39, 144)-Net over F₂ — Constructive and digital

Digital (119, 158, 144)-net over F₂, using

4 times m-reduction [i] based on digital (119, 162, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 54, 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]

(119, 119+39, 239)-Net over F₂ — Digital

Digital (119, 158, 239)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+39, 2408)-Net in Base 2 — Upper bound on s

There is no (119, 158, 2409)-net in base 2, because

1 times m-reduction [i] would yield (119, 157, 2409)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 183936 387384 142063 145649 030992 345030 361742 239280 > 2¹⁵⁷ [i]