MinT - Best Known (217−58, 217, s)-Nets in Base 2

Best Known (217−58, 217, s)-Nets in Base 2

(217−58, 217, 195)-Net over F₂ — Constructive and digital

Digital (159, 217, 195)-net over F₂, using

2¹ times duplication [i] based on digital (158, 216, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 72, 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]

(217−58, 217, 252)-Net over F₂ — Digital

Digital (159, 217, 252)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−58, 217, 2045)-Net in Base 2 — Upper bound on s

There is no (159, 217, 2046)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 213432 441812 467287 166632 925791 114901 342904 412988 030660 683779 031773 > 2²¹⁷ [i]