MinT - Best Known (177−74, 177, s)-Nets in Base 2

Best Known (177−74, 177, s)-Nets in Base 2

(177−74, 177, 60)-Net over F₂ — Constructive and digital

Digital (103, 177, 60)-net over F₂, using

3 times m-reduction [i] based on digital (103, 180, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 90, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(177−74, 177, 75)-Net over F₂ — Digital

Digital (103, 177, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−74, 177, 351)-Net in Base 2 — Upper bound on s

There is no (103, 177, 352)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 194938 347779 480217 502895 132661 876812 172501 941822 336322 > 2¹⁷⁷ [i]