MinT - Best Known (193−73, 193, s)-Nets in Base 2

Best Known (193−73, 193, s)-Nets in Base 2

(193−73, 193, 68)-Net over F₂ — Constructive and digital

Digital (120, 193, 68)-net over F₂, using

5 times m-reduction [i] based on digital (120, 198, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 99, 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]

(193−73, 193, 102)-Net over F₂ — Digital

Digital (120, 193, 102)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−73, 193, 524)-Net in Base 2 — Upper bound on s

There is no (120, 193, 525)-net in base 2, because

1 times m-reduction [i] would yield (120, 192, 525)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6514 039377 519756 747608 770235 471722 901260 540162 905964 794192 > 2¹⁹² [i]