MinT - Best Known (164−47, 164, s)-Nets in Base 3

Best Known (164−47, 164, s)-Nets in Base 3

(164−47, 164, 246)-Net over F₃ — Constructive and digital

Digital (117, 164, 246)-net over F₃, using

1 times m-reduction [i] based on digital (117, 165, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 55, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(164−47, 164, 436)-Net over F₃ — Digital

Digital (117, 164, 436)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−47, 164, 11321)-Net in Base 3 — Upper bound on s

There is no (117, 164, 11322)-net in base 3, because

1 times m-reduction [i] would yield (117, 163, 11322)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 590530 485475 979544 955856 732904 756866 905664 513701 421428 693340 259608 195206 298601 > 3¹⁶³ [i]