MinT - Best Known (74−24, 74, s)-Nets in Base 3

Best Known (74−24, 74, s)-Nets in Base 3

(74−24, 74, 128)-Net over F₃ — Constructive and digital

Digital (50, 74, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 37, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(74−24, 74, 157)-Net over F₃ — Digital

Digital (50, 74, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−24, 74, 2303)-Net in Base 3 — Upper bound on s

There is no (50, 74, 2304)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 203098 463683 168546 588807 181670 029313 > 3⁷⁴ [i]