MinT - Best Known (95, 162, s)-Nets in Base 2

Best Known (95, 162, s)-Nets in Base 2

(95, 162, 60)-Net over F₂ — Constructive and digital

Digital (95, 162, 60)-net over F₂, using

2 times m-reduction [i] based on digital (95, 164, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 82, 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]

(95, 162, 72)-Net over F₂ — Digital

Digital (95, 162, 72)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 162, 340)-Net in Base 2 — Upper bound on s

There is no (95, 162, 341)-net in base 2, because

1 times m-reduction [i] would yield (95, 161, 341)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 942768 716272 380818 279340 700532 355613 868241 346140 > 2¹⁶¹ [i]