MinT - Best Known (123−50, 123, s)-Nets in Base 2

Best Known (123−50, 123, s)-Nets in Base 2

(123−50, 123, 54)-Net over F₂ — Constructive and digital

Digital (73, 123, 54)-net over F₂, using

3 times m-reduction [i] based on digital (73, 126, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 63, 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]

(123−50, 123, 60)-Net over F₂ — Digital

Digital (73, 123, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−50, 123, 273)-Net in Base 2 — Upper bound on s

There is no (73, 123, 274)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 533908 255778 068099 440932 239051 836512 > 2¹²³ [i]