MinT - Best Known (154−42, 154, s)-Nets in Base 2

Best Known (154−42, 154, s)-Nets in Base 2

(154−42, 154, 135)-Net over F₂ — Constructive and digital

Digital (112, 154, 135)-net over F₂, using

2¹ times duplication [i] based on digital (111, 153, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 51, 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]

(154−42, 154, 181)-Net over F₂ — Digital

Digital (112, 154, 181)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−42, 154, 1369)-Net in Base 2 — Upper bound on s

There is no (112, 154, 1370)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23165 701466 538965 255715 200609 653633 947318 433622 > 2¹⁵⁴ [i]