MinT - Best Known (73−23, 73, s)-Nets in Base 2

Best Known (73−23, 73, s)-Nets in Base 2

(73−23, 73, 60)-Net over F₂ — Constructive and digital

Digital (50, 73, 60)-net over F₂, using

1 times m-reduction [i] based on digital (50, 74, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 37, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(73−23, 73, 74)-Net over F₂ — Digital

Digital (50, 73, 74)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−23, 73, 442)-Net in Base 2 — Upper bound on s

There is no (50, 73, 443)-net in base 2, because

1 times m-reduction [i] would yield (50, 72, 443)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4744 840332 061221 232146 > 2⁷² [i]