MinT - Best Known (172, 172+72, s)-Nets in Base 2

Best Known (172, 172+72, s)-Nets in Base 2

(172, 172+72, 135)-Net over F₂ — Constructive and digital

Digital (172, 244, 135)-net over F₂, using

2¹ times duplication [i] based on digital (171, 243, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 81, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(172, 172+72, 220)-Net over F₂ — Digital

Digital (172, 244, 220)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+72, 1514)-Net in Base 2 — Upper bound on s

There is no (172, 244, 1515)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 755362 892332 681158 258021 839954 318815 496283 294491 448939 450438 934978 627126 > 2²⁴⁴ [i]