MinT - Best Known (166−45, 166, s)-Nets in Base 3

Best Known (166−45, 166, s)-Nets in Base 3

(166−45, 166, 282)-Net over F₃ — Constructive and digital

Digital (121, 166, 282)-net over F₃, using

3¹ times duplication [i] based on digital (120, 165, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 55, 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]

(166−45, 166, 537)-Net over F₃ — Digital

Digital (121, 166, 537)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−45, 166, 17127)-Net in Base 3 — Upper bound on s

There is no (121, 166, 17128)-net in base 3, because

1 times m-reduction [i] would yield (121, 165, 17128)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 313971 373071 304455 297643 081107 896011 761262 216233 439231 824113 246665 639914 282097 > 3¹⁶⁵ [i]