MinT - Best Known (162, 162+49, s)-Nets in Base 3

Best Known (162, 162+49, s)-Nets in Base 3

(162, 162+49, 464)-Net over F₃ — Constructive and digital

Digital (162, 211, 464)-net over F₃, using

t-expansion [i] based on digital (161, 211, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (161, 212, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 53, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(162, 162+49, 1196)-Net over F₃ — Digital

Digital (162, 211, 1196)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+49, 73283)-Net in Base 3 — Upper bound on s

There is no (162, 211, 73284)-net in base 3, because

1 times m-reduction [i] would yield (162, 210, 73284)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15688 289505 775739 855037 929363 821879 709253 329386 530356 201351 145068 995246 490985 750900 326698 923854 841921 > 3²¹⁰ [i]