MinT - Best Known (130, 130+79, s)-Nets in Base 3

Best Known (130, 130+79, s)-Nets in Base 3

(130, 130+79, 156)-Net over F₃ — Constructive and digital

Digital (130, 209, 156)-net over F₃, using

7 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+79, 228)-Net over F₃ — Digital

Digital (130, 209, 228)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+79, 2659)-Net in Base 3 — Upper bound on s

There is no (130, 209, 2660)-net in base 3, because

1 times m-reduction [i] would yield (130, 208, 2660)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1749 567616 436619 249711 209913 492667 468532 719395 371732 825610 767345 701144 889470 926932 428428 334942 015345 > 3²⁰⁸ [i]