MinT - Best Known (114, 114+95, s)-Nets in Base 3

Best Known (114, 114+95, s)-Nets in Base 3

(114, 114+95, 80)-Net over F₃ — Constructive and digital

Digital (114, 209, 80)-net over F₃, using

3 times m-reduction [i] based on digital (114, 212, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 106, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(114, 114+95, 136)-Net over F₃ — Digital

Digital (114, 209, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+95, 1141)-Net in Base 3 — Upper bound on s

There is no (114, 209, 1142)-net in base 3, because

1 times m-reduction [i] would yield (114, 208, 1142)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1769 830665 840768 020974 964054 566962 596424 404532 983822 099483 674296 083814 606469 340602 102676 291440 927689 > 3²⁰⁸ [i]