MinT - Best Known (136−76, 136, s)-Nets in Base 9

Best Known (136−76, 136, s)-Nets in Base 9

(136−76, 136, 106)-Net over F₉ — Constructive and digital

Digital (60, 136, 106)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 43, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 93, 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]

(136−76, 136, 190)-Net over F₉ — Digital

Digital (60, 136, 190)-net over F₉, using

net from sequence [i] based on digital (60, 189)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 60 and N(F) ≥ 190, using
  - Drinfeld modules of rank 1 [i]

(136−76, 136, 4862)-Net in Base 9 — Upper bound on s

There is no (60, 136, 4863)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6023 727556 343969 551199 402016 601589 550315 001852 382737 151475 997130 898552 841258 259110 820096 902172 137105 306281 425435 232183 733608 050385 > 9¹³⁶ [i]