MinT - Best Known (145−58, 145, s)-Nets in Base 2

Best Known (145−58, 145, s)-Nets in Base 2

(145−58, 145, 60)-Net over F₂ — Constructive and digital

Digital (87, 145, 60)-net over F₂, using

3 times m-reduction [i] based on digital (87, 148, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 74, 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]

(145−58, 145, 71)-Net over F₂ — Digital

Digital (87, 145, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−58, 145, 332)-Net in Base 2 — Upper bound on s

There is no (87, 145, 333)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 45 977205 024352 711020 334371 282815 673632 830760 > 2¹⁴⁵ [i]