MinT - Best Known (227−65, 227, s)-Nets in Base 3

Best Known (227−65, 227, s)-Nets in Base 3

(227−65, 227, 282)-Net over F₃ — Constructive and digital

Digital (162, 227, 282)-net over F₃, using

1 times m-reduction [i] based on digital (162, 228, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 76, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(227−65, 227, 576)-Net over F₃ — Digital

Digital (162, 227, 576)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−65, 227, 14948)-Net in Base 3 — Upper bound on s

There is no (162, 227, 14949)-net in base 3, because

1 times m-reduction [i] would yield (162, 226, 14949)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675467 338521 999236 064048 600660 607011 590517 329920 668696 771121 812661 815712 240807 334274 130611 609232 198774 019969 > 3²²⁶ [i]