MinT - Best Known (207−81, 207, s)-Nets in Base 2

Best Known (207−81, 207, s)-Nets in Base 2

(207−81, 207, 68)-Net over F₂ — Constructive and digital

Digital (126, 207, 68)-net over F₂, using

3 times m-reduction [i] based on digital (126, 210, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 105, 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]

(207−81, 207, 100)-Net over F₂ — Digital

Digital (126, 207, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−81, 207, 503)-Net in Base 2 — Upper bound on s

There is no (126, 207, 504)-net in base 2, because

1 times m-reduction [i] would yield (126, 206, 504)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 109 580939 077026 044159 207342 717032 069823 275902 268168 403541 530466 > 2²⁰⁶ [i]