MinT - Best Known (90, 90+150, s)-Nets in Base 3

Best Known (90, 90+150, s)-Nets in Base 3

(90, 90+150, 64)-Net over F₃ — Constructive and digital

Digital (90, 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]

(90, 90+150, 96)-Net over F₃ — Digital

Digital (90, 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]

(90, 90+150, 413)-Net in Base 3 — Upper bound on s

There is no (90, 240, 414)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 566614 878080 331649 207256 376429 653737 076436 101798 095515 543013 538001 617384 256011 354334 927503 173447 892187 879088 967601 > 3²⁴⁰ [i]