MinT - Best Known (240−147, 240, s)-Nets in Base 3

Best Known (240−147, 240, s)-Nets in Base 3

(240−147, 240, 64)-Net over F₃ — Constructive and digital

Digital (93, 240, 64)-net over F₃, using

t-expansion [i] based on digital (89, 240, 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]

(240−147, 240, 96)-Net over F₃ — Digital

Digital (93, 240, 96)-net over F₃, using

t-expansion [i] based on digital (89, 240, 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]

(240−147, 240, 442)-Net in Base 3 — Upper bound on s

There is no (93, 240, 443)-net in base 3, because

1 times m-reduction [i] would yield (93, 239, 443)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 180894 211288 808727 968092 790214 068786 840627 824451 783221 095383 024776 759687 938280 001568 932561 802206 894563 243848 540071 > 3²³⁹ [i]