MinT - Best Known (89, 113, s)-Nets in Base 2

Best Known (89, 113, s)-Nets in Base 2

(89, 113, 180)-Net over F₂ — Constructive and digital

Digital (89, 113, 180)-net over F₂, using

2¹ times duplication [i] based on digital (88, 112, 180)-net over F₂, using
- trace code for nets [i] based on digital (4, 28, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(89, 113, 282)-Net over F₂ — Digital

Digital (89, 113, 282)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 113, 3597)-Net in Base 2 — Upper bound on s

There is no (89, 113, 3598)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10414 263660 969735 662300 879499 404093 > 2¹¹³ [i]