MinT - Best Known (149−51, 149, s)-Nets in Base 3

Best Known (149−51, 149, s)-Nets in Base 3

(149−51, 149, 156)-Net over F₃ — Constructive and digital

Digital (98, 149, 156)-net over F₃, using

3 times m-reduction [i] based on digital (98, 152, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 76, 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]

(149−51, 149, 229)-Net over F₃ — Digital

Digital (98, 149, 229)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−51, 149, 3373)-Net in Base 3 — Upper bound on s

There is no (98, 149, 3374)-net in base 3, because

1 times m-reduction [i] would yield (98, 148, 3374)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41404 834920 216597 160846 515677 917170 700091 745623 929380 636546 284676 623021 > 3¹⁴⁸ [i]