MinT - Best Known (97−49, 97, s)-Nets in Base 9

Best Known (97−49, 97, s)-Nets in Base 9

(97−49, 97, 110)-Net over F₉ — Constructive and digital

Digital (48, 97, 110)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (7, 31, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]
2. digital (17, 66, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(97−49, 97, 185)-Net over F₉ — Digital

Digital (48, 97, 185)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−49, 97, 8025)-Net in Base 9 — Upper bound on s

There is no (48, 97, 8026)-net in base 9, because

1 times m-reduction [i] would yield (48, 96, 8026)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 573012 532482 863430 236033 999304 434461 138895 289319 876394 489960 428448 762374 607873 068049 587841 > 9⁹⁶ [i]