MinT - Best Known (75−25, 75, s)-Nets in Base 2

Best Known (75−25, 75, s)-Nets in Base 2

(75−25, 75, 56)-Net over F₂ — Constructive and digital

Digital (50, 75, 56)-net over F₂, using

1 times m-reduction [i] based on digital (50, 76, 56)-net over F₂, using
- trace code for nets [i] based on digital (12, 38, 28)-net over F₄, using
  - net from sequence [i] based on digital (12, 27)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(75−25, 75, 65)-Net over F₂ — Digital

Digital (50, 75, 65)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−25, 75, 362)-Net in Base 2 — Upper bound on s

There is no (50, 75, 363)-net in base 2, because

1 times m-reduction [i] would yield (50, 74, 363)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19013 685733 347590 728224 > 2⁷⁴ [i]