MinT - Best Known (206−61, 206, s)-Nets in Base 2

Best Known (206−61, 206, s)-Nets in Base 2

(206−61, 206, 112)-Net over F₂ — Constructive and digital

Digital (145, 206, 112)-net over F₂, using

18 times m-reduction [i] based on digital (145, 224, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 112, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(206−61, 206, 189)-Net over F₂ — Digital

Digital (145, 206, 189)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−61, 206, 1329)-Net in Base 2 — Upper bound on s

There is no (145, 206, 1330)-net in base 2, because

1 times m-reduction [i] would yield (145, 205, 1330)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 51 824871 458092 372975 094097 196808 365888 610313 680644 654837 029360 > 2²⁰⁵ [i]