MinT - Best Known (158, 158+87, s)-Nets in Base 3

Best Known (158, 158+87, s)-Nets in Base 3

(158, 158+87, 162)-Net over F₃ — Constructive and digital

Digital (158, 245, 162)-net over F₃, using

t-expansion [i] based on digital (157, 245, 162)-net over F₃, using
- 5 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+87, 314)-Net over F₃ — Digital

Digital (158, 245, 314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+87, 4261)-Net in Base 3 — Upper bound on s

There is no (158, 245, 4262)-net in base 3, because

1 times m-reduction [i] would yield (158, 244, 4262)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 263 671883 307898 254523 923016 529339 131204 144942 380109 411813 782942 045406 073855 897862 783655 108997 898740 827376 606248 526673 > 3²⁴⁴ [i]