MinT - Best Known (116, 116+79, s)-Nets in Base 3

Best Known (116, 116+79, s)-Nets in Base 3

(116, 116+79, 148)-Net over F₃ — Constructive and digital

Digital (116, 195, 148)-net over F₃, using

3 times m-reduction [i] based on digital (116, 198, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 99, 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]

(116, 116+79, 176)-Net over F₃ — Digital

Digital (116, 195, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+79, 1780)-Net in Base 3 — Upper bound on s

There is no (116, 195, 1781)-net in base 3, because

1 times m-reduction [i] would yield (116, 194, 1781)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 367 777078 264900 044717 165090 732211 908606 830499 624628 211452 136015 647310 004380 198939 189540 981275 > 3¹⁹⁴ [i]