MinT - Best Known (145, 145+73, s)-Nets in Base 3

Best Known (145, 145+73, s)-Nets in Base 3

(145, 145+73, 162)-Net over F₃ — Constructive and digital

Digital (145, 218, 162)-net over F₃, using

8 times m-reduction [i] based on digital (145, 226, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 113, 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]

(145, 145+73, 338)-Net over F₃ — Digital

Digital (145, 218, 338)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+73, 5331)-Net in Base 3 — Upper bound on s

There is no (145, 218, 5332)-net in base 3, because

1 times m-reduction [i] would yield (145, 217, 5332)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 518663 884308 949395 548694 017658 726482 244782 436887 462681 282299 076235 124835 753669 980933 107249 927681 063745 > 3²¹⁷ [i]