MinT - Best Known (56, 56+37, s)-Nets in Base 2

Best Known (56, 56+37, s)-Nets in Base 2

(56, 56+37, 44)-Net over F₂ — Constructive and digital

Digital (56, 93, 44)-net over F₂, using

1 times m-reduction [i] based on digital (56, 94, 44)-net over F₂, using
- trace code for nets [i] based on digital (9, 47, 22)-net over F₄, using
  - net from sequence [i] based on digital (9, 21)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
      - an explicitly constructive algebraic function field [i]

(56, 56+37, 52)-Net over F₂ — Digital

Digital (56, 93, 52)-net over F₂, using

1 times m-reduction [i] based on digital (56, 94, 52)-net over F₂, using
- trace code for nets [i] based on digital (9, 47, 26)-net over F₄, using
  - net from sequence [i] based on digital (9, 25)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
      - Drinfeld modules of rank 1 [i]

(56, 56+37, 235)-Net in Base 2 — Upper bound on s

There is no (56, 93, 236)-net in base 2, because

1 times m-reduction [i] would yield (56, 92, 236)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5051 922097 852206 271156 362034 > 2⁹² [i]