MinT - Best Known (197−57, 197, s)-Nets in Base 3

Best Known (197−57, 197, s)-Nets in Base 3

(197−57, 197, 252)-Net over F₃ — Constructive and digital

Digital (140, 197, 252)-net over F₃, using

1 times m-reduction [i] based on digital (140, 198, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 66, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(197−57, 197, 492)-Net over F₃ — Digital

Digital (140, 197, 492)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−57, 197, 12326)-Net in Base 3 — Upper bound on s

There is no (140, 197, 12327)-net in base 3, because

1 times m-reduction [i] would yield (140, 196, 12327)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3279 282010 902368 802033 142774 494641 180379 060506 420183 220131 265482 541897 624050 997500 582641 644489 > 3¹⁹⁶ [i]