MinT - Best Known (69, 69+24, s)-Nets in Base 3

Best Known (69, 69+24, s)-Nets in Base 3

(69, 69+24, 246)-Net over F₃ — Constructive and digital

Digital (69, 93, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 31, 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]

(69, 69+24, 412)-Net over F₃ — Digital

Digital (69, 93, 412)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+24, 13171)-Net in Base 3 — Upper bound on s

There is no (69, 93, 13172)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 235 716510 928000 606368 372306 958840 486130 677121 > 3⁹³ [i]