MinT - Best Known (64, 64+48, s)-Nets in Base 3

Best Known (64, 64+48, s)-Nets in Base 3

(64, 64+48, 80)-Net over F₃ — Constructive and digital

Digital (64, 112, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 56, 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]

(64, 64+48, 95)-Net over F₃ — Digital

Digital (64, 112, 95)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+48, 802)-Net in Base 3 — Upper bound on s

There is no (64, 112, 803)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 276931 026036 328853 942331 289504 434218 435339 714294 141649 > 3¹¹² [i]