MinT - Best Known (62, 62+33, s)-Nets in Base 2

Best Known (62, 62+33, s)-Nets in Base 2

(62, 62+33, 60)-Net over F₂ — Constructive and digital

Digital (62, 95, 60)-net over F₂, using

3 times m-reduction [i] based on digital (62, 98, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 49, 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]

(62, 62+33, 71)-Net over F₂ — Digital

Digital (62, 95, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+33, 376)-Net in Base 2 — Upper bound on s

There is no (62, 95, 377)-net in base 2, because

1 times m-reduction [i] would yield (62, 94, 377)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20440 170832 819414 382756 751549 > 2⁹⁴ [i]