MinT - Best Known (247−150, 247, s)-Nets in Base 3

Best Known (247−150, 247, s)-Nets in Base 3

(247−150, 247, 64)-Net over F₃ — Constructive and digital

Digital (97, 247, 64)-net over F₃, using

t-expansion [i] based on digital (89, 247, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [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]

(247−150, 247, 96)-Net over F₃ — Digital

Digital (97, 247, 96)-net over F₃, using

t-expansion [i] based on digital (89, 247, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(247−150, 247, 465)-Net in Base 3 — Upper bound on s

There is no (97, 247, 466)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7942 923099 318460 367257 229639 349711 516546 081559 624387 612756 148108 841330 010326 820326 726702 800712 022159 987257 652481 338305 > 3²⁴⁷ [i]