MinT - Best Known (205−59, 205, s)-Nets in Base 3

Best Known (205−59, 205, s)-Nets in Base 3

(205−59, 205, 264)-Net over F₃ — Constructive and digital

Digital (146, 205, 264)-net over F₃, using

3¹ times duplication [i] based on digital (145, 204, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 68, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(205−59, 205, 519)-Net over F₃ — Digital

Digital (146, 205, 519)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−59, 205, 13226)-Net in Base 3 — Upper bound on s

There is no (146, 205, 13227)-net in base 3, because

1 times m-reduction [i] would yield (146, 204, 13227)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 517611 202398 228847 977592 786164 854748 302318 328894 379602 927185 219168 878888 562452 541827 022054 349087 > 3²⁰⁴ [i]