MinT - Best Known (88−33, 88, s)-Nets in Base 3

Best Known (88−33, 88, s)-Nets in Base 3

(88−33, 88, 80)-Net over F₃ — Constructive and digital

Digital (55, 88, 80)-net over F₃, using

6 times m-reduction [i] based on digital (55, 94, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 47, 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]

(88−33, 88, 116)-Net over F₃ — Digital

Digital (55, 88, 116)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−33, 88, 1320)-Net in Base 3 — Upper bound on s

There is no (55, 88, 1321)-net in base 3, because

1 times m-reduction [i] would yield (55, 87, 1321)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 324320 713554 295696 304919 156156 909466 363713 > 3⁸⁷ [i]