MinT - Best Known (109, 109+29, s)-Nets in Base 2

Best Known (109, 109+29, s)-Nets in Base 2

(109, 109+29, 196)-Net over F₂ — Constructive and digital

Digital (109, 138, 196)-net over F₂, using

2² times duplication [i] based on digital (107, 136, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 34, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(109, 109+29, 336)-Net over F₂ — Digital

Digital (109, 138, 336)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+29, 5315)-Net in Base 2 — Upper bound on s

There is no (109, 138, 5316)-net in base 2, because

1 times m-reduction [i] would yield (109, 137, 5316)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 174237 782582 227875 982936 761172 981582 071984 > 2¹³⁷ [i]