MinT - Best Known (122−44, 122, s)-Nets in Base 3

Best Known (122−44, 122, s)-Nets in Base 3

(122−44, 122, 148)-Net over F₃ — Constructive and digital

Digital (78, 122, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 61, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(122−44, 122, 167)-Net over F₃ — Digital

Digital (78, 122, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−44, 122, 1981)-Net in Base 3 — Upper bound on s

There is no (78, 122, 1982)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16248 053421 540045 756451 247764 002807 170482 641759 732882 699717 > 3¹²² [i]