MinT - Best Known (98, 98+73, s)-Nets in Base 3

Best Known (98, 98+73, s)-Nets in Base 3

(98, 98+73, 80)-Net over F₃ — Constructive and digital

Digital (98, 171, 80)-net over F₃, using

9 times m-reduction [i] based on digital (98, 180, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 90, 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]

(98, 98+73, 136)-Net over F₃ — Digital

Digital (98, 171, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+73, 1243)-Net in Base 3 — Upper bound on s

There is no (98, 171, 1244)-net in base 3, because

1 times m-reduction [i] would yield (98, 170, 1244)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1303 295621 313245 582810 194589 188821 371903 420678 705518 634063 045689 888058 504825 288193 > 3¹⁷⁰ [i]