MinT - Best Known (193−63, 193, s)-Nets in Base 3

Best Known (193−63, 193, s)-Nets in Base 3

(193−63, 193, 162)-Net over F₃ — Constructive and digital

Digital (130, 193, 162)-net over F₃, using

3 times m-reduction [i] based on digital (130, 196, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 98, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(193−63, 193, 330)-Net over F₃ — Digital

Digital (130, 193, 330)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−63, 193, 5568)-Net in Base 3 — Upper bound on s

There is no (130, 193, 5569)-net in base 3, because

1 times m-reduction [i] would yield (130, 192, 5569)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 678825 272974 408221 232692 311673 378720 167680 665127 528309 634980 272721 903969 314654 149299 151147 > 3¹⁹² [i]