MinT - Best Known (49, 49+68, s)-Nets in Base 9

Best Known (49, 49+68, s)-Nets in Base 9

(49, 49+68, 84)-Net over F₉ — Constructive and digital

Digital (49, 117, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 36, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 81, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(49, 49+68, 94)-Net in Base 9 — Constructive

(49, 117, 94)-net in base 9, using

base change [i] based on digital (10, 78, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(49, 49+68, 168)-Net over F₉ — Digital

Digital (49, 117, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(49, 49+68, 3230)-Net in Base 9 — Upper bound on s

There is no (49, 117, 3231)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4433 034288 726902 455555 107768 017421 626811 398963 855631 343262 362054 019845 152321 304291 966571 800616 442597 209624 319217 > 9¹¹⁷ [i]