MinT - Best Known (172−48, 172, s)-Nets in Base 2

Best Known (172−48, 172, s)-Nets in Base 2

(172−48, 172, 135)-Net over F₂ — Constructive and digital

Digital (124, 172, 135)-net over F₂, using

2¹ times duplication [i] based on digital (123, 171, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 57, 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]

(172−48, 172, 187)-Net over F₂ — Digital

Digital (124, 172, 187)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−48, 172, 1373)-Net in Base 2 — Upper bound on s

There is no (124, 172, 1374)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6051 699594 179786 937449 083812 213038 352450 822815 330927 > 2¹⁷² [i]