MinT - Best Known (101−37, 101, s)-Nets in Base 2

Best Known (101−37, 101, s)-Nets in Base 2

(101−37, 101, 60)-Net over F₂ — Constructive and digital

Digital (64, 101, 60)-net over F₂, using

1 times m-reduction [i] based on digital (64, 102, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 51, 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]

(101−37, 101, 66)-Net over F₂ — Digital

Digital (64, 101, 66)-net over F₂, using

1 times m-reduction [i] based on digital (64, 102, 66)-net over F₂, using
- trace code for nets [i] based on digital (13, 51, 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]

(101−37, 101, 329)-Net in Base 2 — Upper bound on s

There is no (64, 101, 330)-net in base 2, because

1 times m-reduction [i] would yield (64, 100, 330)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 293610 364945 975965 521513 921808 > 2¹⁰⁰ [i]