MinT - Best Known (208−81, 208, s)-Nets in Base 2

Best Known (208−81, 208, s)-Nets in Base 2

(208−81, 208, 68)-Net over F₂ — Constructive and digital

Digital (127, 208, 68)-net over F₂, using

4 times m-reduction [i] based on digital (127, 212, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 106, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(208−81, 208, 101)-Net over F₂ — Digital

Digital (127, 208, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−81, 208, 512)-Net in Base 2 — Upper bound on s

There is no (127, 208, 513)-net in base 2, because

1 times m-reduction [i] would yield (127, 207, 513)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 207 766093 747726 496900 433886 215454 112416 655600 892783 331636 926656 > 2²⁰⁷ [i]