MinT - Best Known (119, 162, s)-Nets in Base 2

Best Known (119, 162, s)-Nets in Base 2

(119, 162, 144)-Net over F₂ — Constructive and digital

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, 162, 202)-Net over F₂ — Digital

Digital (119, 162, 202)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 162, 1732)-Net in Base 2 — Upper bound on s

There is no (119, 162, 1733)-net in base 2, because

1 times m-reduction [i] would yield (119, 161, 1733)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 929910 332214 347403 379722 343180 718490 967048 706152 > 2¹⁶¹ [i]