MinT - Best Known (166−49, 166, s)-Nets in Base 3

Best Known (166−49, 166, s)-Nets in Base 3

(166−49, 166, 228)-Net over F₃ — Constructive and digital

Digital (117, 166, 228)-net over F₃, using

3¹ times duplication [i] based on digital (116, 165, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 55, 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]

(166−49, 166, 398)-Net over F₃ — Digital

Digital (117, 166, 398)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−49, 166, 9320)-Net in Base 3 — Upper bound on s

There is no (117, 166, 9321)-net in base 3, because

1 times m-reduction [i] would yield (117, 165, 9321)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 312908 498256 507011 830734 372177 542684 893417 069065 809246 162973 427357 652103 276001 > 3¹⁶⁵ [i]