MinT - Best Known (208−61, 208, s)-Nets in Base 2

Best Known (208−61, 208, s)-Nets in Base 2

(208−61, 208, 112)-Net over F₂ — Constructive and digital

Digital (147, 208, 112)-net over F₂, using

20 times m-reduction [i] based on digital (147, 228, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 114, 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]

(208−61, 208, 195)-Net over F₂ — Digital

Digital (147, 208, 195)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−61, 208, 1394)-Net in Base 2 — Upper bound on s

There is no (147, 208, 1395)-net in base 2, because

1 times m-reduction [i] would yield (147, 207, 1395)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 207 531453 577821 065100 730708 381928 586687 305367 683534 209737 138920 > 2²⁰⁷ [i]