MinT - Best Known (137, 230, s)-Nets in Base 3

Best Known (137, 230, s)-Nets in Base 3

(137, 230, 156)-Net over F₃ — Constructive and digital

Digital (137, 230, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 115, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(137, 230, 205)-Net over F₃ — Digital

Digital (137, 230, 205)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 230, 2090)-Net in Base 3 — Upper bound on s

There is no (137, 230, 2091)-net in base 3, because

1 times m-reduction [i] would yield (137, 229, 2091)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 595377 508628 037246 254627 537568 556912 952831 354982 761151 376550 047007 737048 409346 578514 804775 521870 238828 175901 > 3²²⁹ [i]