MinT - Best Known (97, 97+133, s)-Nets in Base 3

Best Known (97, 97+133, s)-Nets in Base 3

(97, 97+133, 64)-Net over F₃ — Constructive and digital

Digital (97, 230, 64)-net over F₃, using

t-expansion [i] based on digital (89, 230, 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]

(97, 97+133, 96)-Net over F₃ — Digital

Digital (97, 230, 96)-net over F₃, using

t-expansion [i] based on digital (89, 230, 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]

(97, 97+133, 512)-Net in Base 3 — Upper bound on s

There is no (97, 230, 513)-net in base 3, because

1 times m-reduction [i] would yield (97, 229, 513)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19 901543 294325 662445 560680 371390 151607 117817 464056 571287 562141 598818 313306 013021 492550 361620 421124 897087 797513 > 3²²⁹ [i]