MinT - Best Known (167−51, 167, s)-Nets in Base 3

Best Known (167−51, 167, s)-Nets in Base 3

(167−51, 167, 192)-Net over F₃ — Constructive and digital

Digital (116, 167, 192)-net over F₃, using

1 times m-reduction [i] based on digital (116, 168, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 56, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(167−51, 167, 359)-Net over F₃ — Digital

Digital (116, 167, 359)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−51, 167, 7468)-Net in Base 3 — Upper bound on s

There is no (116, 167, 7469)-net in base 3, because

1 times m-reduction [i] would yield (116, 166, 7469)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15 928451 601337 218109 896127 758264 511918 645039 709960 188551 647797 154039 653069 301499 > 3¹⁶⁶ [i]