MinT - Best Known (193−59, 193, s)-Nets in Base 3

Best Known (193−59, 193, s)-Nets in Base 3

(193−59, 193, 204)-Net over F₃ — Constructive and digital

Digital (134, 193, 204)-net over F₃, using

3¹ times duplication [i] based on digital (133, 192, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 64, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(193−59, 193, 405)-Net over F₃ — Digital

Digital (134, 193, 405)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−59, 193, 8384)-Net in Base 3 — Upper bound on s

There is no (134, 193, 8385)-net in base 3, because

1 times m-reduction [i] would yield (134, 192, 8385)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 513059 105891 231530 669222 784788 439576 692191 769927 522804 842376 659339 219612 931473 661578 879763 > 3¹⁹² [i]