MinT - Best Known (76, 76+36, s)-Nets in Base 2

Best Known (76, 76+36, s)-Nets in Base 2

(76, 76+36, 66)-Net over F₂ — Constructive and digital

Digital (76, 112, 66)-net over F₂, using

10 times m-reduction [i] based on digital (76, 122, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 61, 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]

(76, 76+36, 95)-Net over F₂ — Digital

Digital (76, 112, 95)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+36, 537)-Net in Base 2 — Upper bound on s

There is no (76, 112, 538)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5199 550442 234058 328422 935423 198164 > 2¹¹² [i]