MinT - Best Known (169−63, 169, s)-Nets in Base 2

Best Known (169−63, 169, s)-Nets in Base 2

(169−63, 169, 68)-Net over F₂ — Constructive and digital

Digital (106, 169, 68)-net over F₂, using

1 times m-reduction [i] based on digital (106, 170, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 85, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(169−63, 169, 94)-Net over F₂ — Digital

Digital (106, 169, 94)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−63, 169, 487)-Net in Base 2 — Upper bound on s

There is no (106, 169, 488)-net in base 2, because

1 times m-reduction [i] would yield (106, 168, 488)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 393 504968 202822 900257 011649 591584 529304 680655 149556 > 2¹⁶⁸ [i]