MinT - Best Known (177−72, 177, s)-Nets in Base 2

Best Known (177−72, 177, s)-Nets in Base 2

(177−72, 177, 66)-Net over F₂ — Constructive and digital

Digital (105, 177, 66)-net over F₂, using

3 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]

(177−72, 177, 80)-Net over F₂ — Digital

Digital (105, 177, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−72, 177, 380)-Net in Base 2 — Upper bound on s

There is no (105, 177, 381)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 197058 589127 248925 638200 196476 700965 244362 242709 431207 > 2¹⁷⁷ [i]