MinT - Best Known (240−152, 240, s)-Nets in Base 3

Best Known (240−152, 240, s)-Nets in Base 3

(240−152, 240, 63)-Net over F₃ — Constructive and digital

Digital (88, 240, 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]

(240−152, 240, 84)-Net over F₃ — Digital

Digital (88, 240, 84)-net over F₃, using

t-expansion [i] based on digital (71, 240, 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]

(240−152, 240, 396)-Net in Base 3 — Upper bound on s

There is no (88, 240, 397)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 386543 967861 306057 465956 642967 256102 377292 277562 104023 862115 095787 721403 185416 600695 165459 470285 548711 639084 478065 > 3²⁴⁰ [i]