MinT - Best Known (163−67, 163, s)-Nets in Base 2

Best Known (163−67, 163, s)-Nets in Base 2

(163−67, 163, 60)-Net over F₂ — Constructive and digital

Digital (96, 163, 60)-net over F₂, using

3 times m-reduction [i] based on digital (96, 166, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 83, 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]

(163−67, 163, 73)-Net over F₂ — Digital

Digital (96, 163, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−67, 163, 349)-Net in Base 2 — Upper bound on s

There is no (96, 163, 350)-net in base 2, because

1 times m-reduction [i] would yield (96, 162, 350)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 309416 661643 218793 733299 339761 974531 671135 962830 > 2¹⁶² [i]