MinT - Best Known (130, 130+71, s)-Nets in Base 3

Best Known (130, 130+71, s)-Nets in Base 3

(130, 130+71, 156)-Net over F₃ — Constructive and digital

Digital (130, 201, 156)-net over F₃, using

15 times m-reduction [i] based on digital (130, 216, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 108, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(130, 130+71, 268)-Net over F₃ — Digital

Digital (130, 201, 268)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+71, 3669)-Net in Base 3 — Upper bound on s

There is no (130, 201, 3670)-net in base 3, because

1 times m-reduction [i] would yield (130, 200, 3670)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 267180 821817 926420 888453 881191 483703 684142 626377 068775 201034 965073 397729 464022 983285 269406 262625 > 3²⁰⁰ [i]