MinT - Best Known (130, 130+87, s)-Nets in Base 3

Best Known (130, 130+87, s)-Nets in Base 3

(130, 130+87, 148)-Net over F₃ — Constructive and digital

Digital (130, 217, 148)-net over F₃, using

9 times m-reduction [i] based on digital (130, 226, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 113, 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, 130+87, 199)-Net over F₃ — Digital

Digital (130, 217, 199)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+87, 2062)-Net in Base 3 — Upper bound on s

There is no (130, 217, 2063)-net in base 3, because

1 times m-reduction [i] would yield (130, 216, 2063)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 595165 239475 873191 235427 878234 066385 857755 836076 470311 543874 034304 880708 613918 112173 672703 929594 899947 > 3²¹⁶ [i]