MinT - Best Known (127−98, 127, s)-Nets in Base 9

Best Known (127−98, 127, s)-Nets in Base 9

(127−98, 127, 78)-Net over F₉ — Constructive and digital

Digital (29, 127, 78)-net over F₉, using

t-expansion [i] based on digital (22, 127, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(127−98, 127, 110)-Net over F₉ — Digital

Digital (29, 127, 110)-net over F₉, using

t-expansion [i] based on digital (26, 127, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(127−98, 127, 680)-Net in Base 9 — Upper bound on s

There is no (29, 127, 681)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 909804 943822 967760 114194 401120 590830 127876 421110 667605 795193 409904 360084 195206 654814 581021 243640 987822 986899 359398 744265 > 9¹²⁷ [i]