MinT - Best Known (129, 186, s)-Nets in Base 3

Best Known (129, 186, s)-Nets in Base 3

(129, 186, 204)-Net over F₃ — Constructive and digital

Digital (129, 186, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 62, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(129, 186, 389)-Net over F₃ — Digital

Digital (129, 186, 389)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 186, 7996)-Net in Base 3 — Upper bound on s

There is no (129, 186, 7997)-net in base 3, because

1 times m-reduction [i] would yield (129, 185, 7997)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18549 958878 847819 176669 514683 897974 925365 724337 938603 654491 448503 249873 978416 624865 306801 > 3¹⁸⁵ [i]