MinT - Best Known (130−60, 130, s)-Nets in Base 3

Best Known (130−60, 130, s)-Nets in Base 3

(130−60, 130, 64)-Net over F₃ — Constructive and digital

Digital (70, 130, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 65, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(130−60, 130, 87)-Net over F₃ — Digital

Digital (70, 130, 87)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−60, 130, 674)-Net in Base 3 — Upper bound on s

There is no (70, 130, 675)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 108 225676 520402 918887 487407 654785 177996 622566 390291 441065 062125 > 3¹³⁰ [i]