MinT - Best Known (128−104, 128, s)-Nets in Base 9

Best Known (128−104, 128, s)-Nets in Base 9

(128−104, 128, 78)-Net over F₉ — Constructive and digital

Digital (24, 128, 78)-net over F₉, using

t-expansion [i] based on digital (22, 128, 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]

(128−104, 128, 92)-Net over F₉ — Digital

Digital (24, 128, 92)-net over F₉, using

t-expansion [i] based on digital (23, 128, 92)-net over F₉, using
- net from sequence [i] based on digital (23, 91)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
    - Drinfeld modules of rank 1 [i]

(128−104, 128, 533)-Net in Base 9 — Upper bound on s

There is no (24, 128, 534)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 151 298177 254928 653405 463737 785625 148138 348687 537167 067209 706221 758181 096063 131379 263793 499378 807215 235638 666827 259011 785025 > 9¹²⁸ [i]