MinT - Best Known (169, 244, s)-Nets in Base 3

Best Known (169, 244, s)-Nets in Base 3

(169, 244, 228)-Net over F₃ — Constructive and digital

Digital (169, 244, 228)-net over F₃, using

3¹ times duplication [i] based on digital (168, 243, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 81, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(169, 244, 489)-Net over F₃ — Digital

Digital (169, 244, 489)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 244, 9926)-Net in Base 3 — Upper bound on s

There is no (169, 244, 9927)-net in base 3, because

1 times m-reduction [i] would yield (169, 243, 9927)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 201570 093751 153374 113321 851943 860363 529992 373209 889119 026992 361246 263945 672089 739352 377408 067933 754516 972745 705863 > 3²⁴³ [i]