MinT - Best Known (158, 158+79, s)-Nets in Base 3

Best Known (158, 158+79, s)-Nets in Base 3

(158, 158+79, 162)-Net over F₃ — Constructive and digital

Digital (158, 237, 162)-net over F₃, using

t-expansion [i] based on digital (157, 237, 162)-net over F₃, using
- 13 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
  - trace code for nets [i] based on digital (32, 125, 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]

(158, 158+79, 369)-Net over F₃ — Digital

Digital (158, 237, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+79, 5898)-Net in Base 3 — Upper bound on s

There is no (158, 237, 5899)-net in base 3, because

1 times m-reduction [i] would yield (158, 236, 5899)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39886 846063 035399 530621 329589 750447 718385 973953 049639 701395 739704 272541 096676 556936 039472 934012 780090 859085 226339 > 3²³⁶ [i]