MinT - Best Known (85, 85+69, s)-Nets in Base 3

Best Known (85, 85+69, s)-Nets in Base 3

(85, 85+69, 80)-Net over F₃ — Constructive and digital

Digital (85, 154, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 77, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(85, 85+69, 109)-Net over F₃ — Digital

Digital (85, 154, 109)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+69, 916)-Net in Base 3 — Upper bound on s

There is no (85, 154, 917)-net in base 3, because

1 times m-reduction [i] would yield (85, 153, 917)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 179059 055199 252827 362582 788217 966311 554043 924565 071241 436861 754064 165745 > 3¹⁵³ [i]