MinT - Best Known (149, 216, s)-Nets in Base 3

Best Known (149, 216, s)-Nets in Base 3

(149, 216, 204)-Net over F₃ — Constructive and digital

Digital (149, 216, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 72, 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]

(149, 216, 427)-Net over F₃ — Digital

Digital (149, 216, 427)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 216, 8417)-Net in Base 3 — Upper bound on s

There is no (149, 216, 8418)-net in base 3, because

1 times m-reduction [i] would yield (149, 215, 8418)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 822391 713553 286512 854253 880923 009380 104379 106984 154636 492019 284844 456204 939254 619338 824607 952627 825285 > 3²¹⁵ [i]