MinT - Best Known (70, 70+44, s)-Nets in Base 3

Best Known (70, 70+44, s)-Nets in Base 3

(70, 70+44, 128)-Net over F₃ — Constructive and digital

Digital (70, 114, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 57, 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]

(70, 70+44, 129)-Net over F₃ — Digital

Digital (70, 114, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+44, 1321)-Net in Base 3 — Upper bound on s

There is no (70, 114, 1322)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 466648 521632 988082 666507 327516 297210 759689 444494 481741 > 3¹¹⁴ [i]