MinT - Best Known (235−83, 235, s)-Nets in Base 3

Best Known (235−83, 235, s)-Nets in Base 3

(235−83, 235, 162)-Net over F₃ — Constructive and digital

Digital (152, 235, 162)-net over F₃, using

5 times m-reduction [i] based on digital (152, 240, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 120, 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]

(235−83, 235, 308)-Net over F₃ — Digital

Digital (152, 235, 308)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−83, 235, 4225)-Net in Base 3 — Upper bound on s

There is no (152, 235, 4226)-net in base 3, because

1 times m-reduction [i] would yield (152, 234, 4226)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4467 619506 471011 182817 918177 751755 887410 017573 452023 587433 828936 663705 247884 220853 388484 324951 329997 595221 885941 > 3²³⁴ [i]