MinT - Best Known (123−33, 123, s)-Nets in Base 3

Best Known (123−33, 123, s)-Nets in Base 3

(123−33, 123, 252)-Net over F₃ — Constructive and digital

Digital (90, 123, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 41, 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]

(123−33, 123, 443)-Net over F₃ — Digital

Digital (90, 123, 443)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−33, 123, 14760)-Net in Base 3 — Upper bound on s

There is no (90, 123, 14761)-net in base 3, because

1 times m-reduction [i] would yield (90, 122, 14761)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16180 889285 524833 453883 283987 697408 252051 494770 242588 575553 > 3¹²² [i]