MinT - Best Known (70, 70+36, s)-Nets in Base 3

Best Known (70, 70+36, s)-Nets in Base 3

(70, 70+36, 148)-Net over F₃ — Constructive and digital

Digital (70, 106, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 53, 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]

(70, 70+36, 178)-Net over F₃ — Digital

Digital (70, 106, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+36, 2419)-Net in Base 3 — Upper bound on s

There is no (70, 106, 2420)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 377 601841 350294 838276 606773 615811 764579 215160 006105 > 3¹⁰⁶ [i]