MinT - Best Known (98−36, 98, s)-Nets in Base 9

Best Known (98−36, 98, s)-Nets in Base 9

(98−36, 98, 448)-Net over F₉ — Constructive and digital

Digital (62, 98, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 49, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(98−36, 98, 834)-Net over F₉ — Digital

Digital (62, 98, 834)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−36, 98, 148022)-Net in Base 9 — Upper bound on s

There is no (62, 98, 148023)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3279 231434 674008 060391 974881 166018 771121 849495 734007 879372 891917 205503 450913 943443 666795 960305 > 9⁹⁸ [i]