MinT - Best Known (203−59, 203, s)-Nets in Base 3

Best Known (203−59, 203, s)-Nets in Base 3

(203−59, 203, 252)-Net over F₃ — Constructive and digital

Digital (144, 203, 252)-net over F₃, using

1 times m-reduction [i] based on digital (144, 204, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 68, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(203−59, 203, 498)-Net over F₃ — Digital

Digital (144, 203, 498)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−59, 203, 12259)-Net in Base 3 — Upper bound on s

There is no (144, 203, 12260)-net in base 3, because

1 times m-reduction [i] would yield (144, 202, 12260)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 392049 245054 684016 321024 793965 978895 645390 547811 375010 020712 590222 156525 083830 341205 419698 508073 > 3²⁰² [i]