MinT - Best Known (118−45, 118, s)-Nets in Base 2

Best Known (118−45, 118, s)-Nets in Base 2

(118−45, 118, 60)-Net over F₂ — Constructive and digital

Digital (73, 118, 60)-net over F₂, using

2 times m-reduction [i] based on digital (73, 120, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 60, 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]

(118−45, 118, 67)-Net over F₂ — Digital

Digital (73, 118, 67)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−45, 118, 330)-Net in Base 2 — Upper bound on s

There is no (73, 118, 331)-net in base 2, because

1 times m-reduction [i] would yield (73, 117, 331)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 176600 363550 027158 864717 008041 297272 > 2¹¹⁷ [i]