MinT - Best Known (90, 129, s)-Nets in Base 3

Best Known (90, 129, s)-Nets in Base 3

(90, 129, 192)-Net over F₃ — Constructive and digital

Digital (90, 129, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 43, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(90, 129, 300)-Net over F₃ — Digital

Digital (90, 129, 300)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 129, 6474)-Net in Base 3 — Upper bound on s

There is no (90, 129, 6475)-net in base 3, because

1 times m-reduction [i] would yield (90, 128, 6475)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 790856 643195 814648 705594 702142 274939 730365 566285 572345 632811 > 3¹²⁸ [i]