MinT - Best Known (235−144, 235, s)-Nets in Base 3

Best Known (235−144, 235, s)-Nets in Base 3

(235−144, 235, 64)-Net over F₃ — Constructive and digital

Digital (91, 235, 64)-net over F₃, using

t-expansion [i] based on digital (89, 235, 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]

(235−144, 235, 96)-Net over F₃ — Digital

Digital (91, 235, 96)-net over F₃, using

t-expansion [i] based on digital (89, 235, 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]

(235−144, 235, 431)-Net in Base 3 — Upper bound on s

There is no (91, 235, 432)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15293 807791 367534 382436 581354 120594 643275 504478 419759 458003 061874 401980 954301 577643 644684 381961 725193 289872 427009 > 3²³⁵ [i]