MinT - Best Known (151, 151+77, s)-Nets in Base 3

Best Known (151, 151+77, s)-Nets in Base 3

(151, 151+77, 162)-Net over F₃ — Constructive and digital

Digital (151, 228, 162)-net over F₃, using

10 times m-reduction [i] based on digital (151, 238, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 119, 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]

(151, 151+77, 342)-Net over F₃ — Digital

Digital (151, 228, 342)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+77, 5283)-Net in Base 3 — Upper bound on s

There is no (151, 228, 5284)-net in base 3, because

1 times m-reduction [i] would yield (151, 227, 5284)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 039731 256874 255138 226567 160830 428298 287430 902010 393472 741264 756617 923049 868489 110107 636797 199057 678821 532825 > 3²²⁷ [i]