MinT - Best Known (183, 183+59, s)-Nets in Base 3

Best Known (183, 183+59, s)-Nets in Base 3

(183, 183+59, 400)-Net over F₃ — Constructive and digital

Digital (183, 242, 400)-net over F₃, using

3² times duplication [i] based on digital (181, 240, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 60, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(183, 183+59, 1099)-Net over F₃ — Digital

Digital (183, 242, 1099)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 183+59, 53815)-Net in Base 3 — Upper bound on s

There is no (183, 242, 53816)-net in base 3, because

1 times m-reduction [i] would yield (183, 241, 53816)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 692340 992868 107785 256377 181945 389789 512462 229339 648653 570234 922511 141264 746248 762871 481010 368888 053600 549170 617457 > 3²⁴¹ [i]