MinT - Best Known (225−67, 225, s)-Nets in Base 3

Best Known (225−67, 225, s)-Nets in Base 3

(225−67, 225, 252)-Net over F₃ — Constructive and digital

Digital (158, 225, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 75, 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]

(225−67, 225, 503)-Net over F₃ — Digital

Digital (158, 225, 503)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−67, 225, 11369)-Net in Base 3 — Upper bound on s

There is no (158, 225, 11370)-net in base 3, because

1 times m-reduction [i] would yield (158, 224, 11370)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75207 000985 761290 290789 260739 161042 557786 980395 203517 441035 430373 649197 581287 826272 478820 010071 590811 014549 > 3²²⁴ [i]