MinT - Best Known (247−85, 247, s)-Nets in Base 2

Best Known (247−85, 247, s)-Nets in Base 2

(247−85, 247, 112)-Net over F₂ — Constructive and digital

Digital (162, 247, 112)-net over F₂, using

11 times m-reduction [i] based on digital (162, 258, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 129, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(247−85, 247, 155)-Net over F₂ — Digital

Digital (162, 247, 155)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−85, 247, 896)-Net in Base 2 — Upper bound on s

There is no (162, 247, 897)-net in base 2, because

1 times m-reduction [i] would yield (162, 246, 897)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 115 845083 492830 281638 128902 866958 090023 787961 321707 993800 043147 995533 110656 > 2²⁴⁶ [i]