MinT - Best Known (112, 112+43, s)-Nets in Base 3

Best Known (112, 112+43, s)-Nets in Base 3

(112, 112+43, 252)-Net over F₃ — Constructive and digital

Digital (112, 155, 252)-net over F₃, using

1 times m-reduction [i] based on digital (112, 156, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 52, 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]

(112, 112+43, 467)-Net over F₃ — Digital

Digital (112, 155, 467)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+43, 13667)-Net in Base 3 — Upper bound on s

There is no (112, 155, 13668)-net in base 3, because

1 times m-reduction [i] would yield (112, 154, 13668)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 974400 952055 820225 147766 441884 612585 742528 626508 604395 794364 096411 556521 > 3¹⁵⁴ [i]