MinT - Best Known (108, 108+29, s)-Nets in Base 2

Best Known (108, 108+29, s)-Nets in Base 2

(108, 108+29, 196)-Net over F₂ — Constructive and digital

Digital (108, 137, 196)-net over F₂, using

2¹ 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]

(108, 108+29, 327)-Net over F₂ — Digital

Digital (108, 137, 327)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+29, 5058)-Net in Base 2 — Upper bound on s

There is no (108, 137, 5059)-net in base 2, because

1 times m-reduction [i] would yield (108, 136, 5059)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 87305 268108 791689 742962 023096 581053 567056 > 2¹³⁶ [i]