MinT - Best Known (114, 114+87, s)-Nets in Base 3

Best Known (114, 114+87, s)-Nets in Base 3

(114, 114+87, 128)-Net over F₃ — Constructive and digital

Digital (114, 201, 128)-net over F₃, using

1 times m-reduction [i] based on digital (114, 202, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 101, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(114, 114+87, 151)-Net over F₃ — Digital

Digital (114, 201, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+87, 1356)-Net in Base 3 — Upper bound on s

There is no (114, 201, 1357)-net in base 3, because

1 times m-reduction [i] would yield (114, 200, 1357)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270959 826305 904042 433126 759364 870410 926993 325126 122998 354570 618767 857057 125306 306954 541181 360491 > 3²⁰⁰ [i]