MinT - Best Known (60, 93, s)-Nets in Base 2

Best Known (60, 93, s)-Nets in Base 2

(60, 93, 60)-Net over F₂ — Constructive and digital

Digital (60, 93, 60)-net over F₂, using

1 times m-reduction [i] based on digital (60, 94, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 47, 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]

(60, 93, 66)-Net over F₂ — Digital

Digital (60, 93, 66)-net over F₂, using

1 times m-reduction [i] based on digital (60, 94, 66)-net over F₂, using
- trace code for nets [i] based on digital (13, 47, 33)-net over F₄, using
  - net from sequence [i] based on digital (13, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 33, using
      - Drinfeld modules of rank 1 [i]

(60, 93, 343)-Net in Base 2 — Upper bound on s

There is no (60, 93, 344)-net in base 2, because

1 times m-reduction [i] would yield (60, 92, 344)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5140 604763 596421 676493 243505 > 2⁹² [i]