MinT - Best Known (67, 90, s)-Nets in Base 3

Best Known (67, 90, s)-Nets in Base 3

(67, 90, 246)-Net over F₃ — Constructive and digital

Digital (67, 90, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 30, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(67, 90, 416)-Net over F₃ — Digital

Digital (67, 90, 416)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 90, 17785)-Net in Base 3 — Upper bound on s

There is no (67, 90, 17786)-net in base 3, because

1 times m-reduction [i] would yield (67, 89, 17786)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 909739 603206 494282 279839 821517 439420 868001 > 3⁸⁹ [i]