MinT - Best Known (98−42, 98, s)-Nets in Base 9

Best Known (98−42, 98, s)-Nets in Base 9

(98−42, 98, 344)-Net over F₉ — Constructive and digital

Digital (56, 98, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 49, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(98−42, 98, 386)-Net over F₉ — Digital

Digital (56, 98, 386)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−42, 98, 30786)-Net in Base 9 — Upper bound on s

There is no (56, 98, 30787)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3280 948094 205557 998231 438334 006634 960680 744907 166633 436262 119179 815806 148759 997731 447404 687097 > 9⁹⁸ [i]