MinT - Best Known (173−68, 173, s)-Nets in Base 2

Best Known (173−68, 173, s)-Nets in Base 2

(173−68, 173, 66)-Net over F₂ — Constructive and digital

Digital (105, 173, 66)-net over F₂, using

7 times m-reduction [i] based on digital (105, 180, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 90, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(173−68, 173, 85)-Net over F₂ — Digital

Digital (105, 173, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−68, 173, 412)-Net in Base 2 — Upper bound on s

There is no (105, 173, 413)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12570 114612 214542 305295 809217 754262 697058 012257 972648 > 2¹⁷³ [i]