MinT - Best Known (215−55, 215, s)-Nets in Base 2

Best Known (215−55, 215, s)-Nets in Base 2

(215−55, 215, 195)-Net over F₂ — Constructive and digital

Digital (160, 215, 195)-net over F₂, using

4 times m-reduction [i] based on digital (160, 219, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 73, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(215−55, 215, 280)-Net over F₂ — Digital

Digital (160, 215, 280)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−55, 215, 2617)-Net in Base 2 — Upper bound on s

There is no (160, 215, 2618)-net in base 2, because

1 times m-reduction [i] would yield (160, 214, 2618)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26594 798964 957440 595734 007991 225301 165671 948199 958264 789656 721308 > 2²¹⁴ [i]