MinT - Best Known (88, 88+138, s)-Nets in Base 3

Best Known (88, 88+138, s)-Nets in Base 3

(88, 88+138, 63)-Net over F₃ — Constructive and digital

Digital (88, 226, 63)-net over F₃, using

net from sequence [i] based on digital (88, 62)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 62)-sequence over F₉, using
  - s-reduction 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]

(88, 88+138, 84)-Net over F₃ — Digital

Digital (88, 226, 84)-net over F₃, using

t-expansion [i] based on digital (71, 226, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(88, 88+138, 419)-Net in Base 3 — Upper bound on s

There is no (88, 226, 420)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 689929 702999 761082 193837 589428 234871 474806 391989 585346 488961 083762 045500 198774 122506 377320 595091 233954 134825 > 3²²⁶ [i]