MinT - Best Known (193−81, 193, s)-Nets in Base 3

Best Known (193−81, 193, s)-Nets in Base 3

(193−81, 193, 128)-Net over F₃ — Constructive and digital

Digital (112, 193, 128)-net over F₃, using

5 times m-reduction [i] based on digital (112, 198, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 99, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(193−81, 193, 158)-Net over F₃ — Digital

Digital (112, 193, 158)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−81, 193, 1498)-Net in Base 3 — Upper bound on s

There is no (112, 193, 1499)-net in base 3, because

1 times m-reduction [i] would yield (112, 192, 1499)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 619954 041323 763970 222726 158020 487074 530491 050659 890445 432379 035988 017800 364620 600925 237041 > 3¹⁹² [i]