MinT - Best Known (242−151, 242, s)-Nets in Base 3

Best Known (242−151, 242, s)-Nets in Base 3

(242−151, 242, 64)-Net over F₃ — Constructive and digital

Digital (91, 242, 64)-net over F₃, using

t-expansion [i] based on digital (89, 242, 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]

(242−151, 242, 96)-Net over F₃ — Digital

Digital (91, 242, 96)-net over F₃, using

t-expansion [i] based on digital (89, 242, 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]

(242−151, 242, 420)-Net in Base 3 — Upper bound on s

There is no (91, 242, 421)-net in base 3, because

1 times m-reduction [i] would yield (91, 241, 421)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 562576 799334 386058 110590 775732 857007 294244 801788 514865 174606 587996 368024 762408 032343 728043 102511 720859 790221 054091 > 3²⁴¹ [i]