MinT - Best Known (127−104, 127, s)-Nets in Base 9

Best Known (127−104, 127, s)-Nets in Base 9

(127−104, 127, 78)-Net over F₉ — Constructive and digital

Digital (23, 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]

(127−104, 127, 92)-Net over F₉ — Digital

Digital (23, 127, 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]

(127−104, 127, 509)-Net in Base 9 — Upper bound on s

There is no (23, 127, 510)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 830375 399685 133386 604721 510654 511031 257796 367210 009804 297953 437152 136906 201154 952763 999269 519823 391629 481588 457281 816641 > 9¹²⁷ [i]