MinT - Best Known (163, 163+49, s)-Nets in Base 3

Best Known (163, 163+49, s)-Nets in Base 3

(163, 163+49, 600)-Net over F₃ — Constructive and digital

Digital (163, 212, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 53, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(163, 163+49, 1223)-Net over F₃ — Digital

Digital (163, 212, 1223)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+49, 76716)-Net in Base 3 — Upper bound on s

There is no (163, 212, 76717)-net in base 3, because

1 times m-reduction [i] would yield (163, 211, 76717)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47054 894616 468424 661111 484265 880956 261464 193056 656960 554545 670216 719959 179508 895004 569420 359951 893281 > 3²¹¹ [i]