MinT - Best Known (130−48, 130, s)-Nets in Base 3

Best Known (130−48, 130, s)-Nets in Base 3

(130−48, 130, 148)-Net over F₃ — Constructive and digital

Digital (82, 130, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 65, 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]

(130−48, 130, 163)-Net over F₃ — Digital

Digital (82, 130, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−48, 130, 1859)-Net in Base 3 — Upper bound on s

There is no (82, 130, 1860)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107 279132 948873 058068 676945 877260 711386 660961 270426 743580 485697 > 3¹³⁰ [i]