MinT - Best Known (75−30, 75, s)-Nets in Base 2

Best Known (75−30, 75, s)-Nets in Base 2

(75−30, 75, 42)-Net over F₂ — Constructive and digital

Digital (45, 75, 42)-net over F₂, using

1 times m-reduction [i] based on digital (45, 76, 42)-net over F₂, using
- trace code for nets [i] based on digital (7, 38, 21)-net over F₄, using
  - net from sequence [i] based on digital (7, 20)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]

(75−30, 75, 43)-Net over F₂ — Digital

Digital (45, 75, 43)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−30, 75, 184)-Net in Base 2 — Upper bound on s

There is no (45, 75, 185)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 39022 405009 707147 791360 > 2⁷⁵ [i]