MinT - Best Known (97, 172, s)-Nets in Base 3

Best Known (97, 172, s)-Nets in Base 3

(97, 172, 80)-Net over F₃ — Constructive and digital

Digital (97, 172, 80)-net over F₃, using

6 times m-reduction [i] based on digital (97, 178, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 89, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(97, 172, 129)-Net over F₃ — Digital

Digital (97, 172, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 172, 1138)-Net in Base 3 — Upper bound on s

There is no (97, 172, 1139)-net in base 3, because

1 times m-reduction [i] would yield (97, 171, 1139)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3901 638806 949269 591673 626668 645724 640499 398503 111836 212174 797844 045561 146896 739487 > 3¹⁷¹ [i]