MinT - Best Known (193−75, 193, s)-Nets in Base 2

Best Known (193−75, 193, s)-Nets in Base 2

(193−75, 193, 68)-Net over F₂ — Constructive and digital

Digital (118, 193, 68)-net over F₂, using

1 times m-reduction [i] based on digital (118, 194, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 97, 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]

(193−75, 193, 96)-Net over F₂ — Digital

Digital (118, 193, 96)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−75, 193, 482)-Net in Base 2 — Upper bound on s

There is no (118, 193, 483)-net in base 2, because

1 times m-reduction [i] would yield (118, 192, 483)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6713 953617 579588 565575 015042 475207 736152 784640 248294 079664 > 2¹⁹² [i]