MinT - Best Known (75−27, 75, s)-Nets in Base 2

Best Known (75−27, 75, s)-Nets in Base 2

(75−27, 75, 54)-Net over F₂ — Constructive and digital

Digital (48, 75, 54)-net over F₂, using

1 times m-reduction [i] based on digital (48, 76, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 38, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(75−27, 75, 55)-Net over F₂ — Digital

Digital (48, 75, 55)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−27, 75, 274)-Net in Base 2 — Upper bound on s

There is no (48, 75, 275)-net in base 2, because

1 times m-reduction [i] would yield (48, 74, 275)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19227 412288 553550 629376 > 2⁷⁴ [i]