MinT - Best Known (55, 55+36, s)-Nets in Base 2

Best Known (55, 55+36, s)-Nets in Base 2

(55, 55+36, 44)-Net over F₂ — Constructive and digital

Digital (55, 91, 44)-net over F₂, using

1 times m-reduction [i] based on digital (55, 92, 44)-net over F₂, using
- trace code for nets [i] based on digital (9, 46, 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]

(55, 55+36, 52)-Net over F₂ — Digital

Digital (55, 91, 52)-net over F₂, using

1 times m-reduction [i] based on digital (55, 92, 52)-net over F₂, using
- trace code for nets [i] based on digital (9, 46, 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]

(55, 55+36, 225)-Net in Base 2 — Upper bound on s

There is no (55, 91, 226)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2495 181584 074921 595103 387104 > 2⁹¹ [i]