MinT - Best Known (130−45, 130, s)-Nets in Base 3

Best Known (130−45, 130, s)-Nets in Base 3

(130−45, 130, 148)-Net over F₃ — Constructive and digital

Digital (85, 130, 148)-net over F₃, using

6 times m-reduction [i] based on digital (85, 136, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 68, 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]

(130−45, 130, 199)-Net over F₃ — Digital

Digital (85, 130, 199)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−45, 130, 2819)-Net in Base 3 — Upper bound on s

There is no (85, 130, 2820)-net in base 3, because

1 times m-reduction [i] would yield (85, 129, 2820)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35 457977 336722 059141 778002 026467 290351 094937 886078 717213 837273 > 3¹²⁹ [i]