MinT - Best Known (115−91, 115, s)-Nets in Base 9

Best Known (115−91, 115, s)-Nets in Base 9

(115−91, 115, 78)-Net over F₉ — Constructive and digital

Digital (24, 115, 78)-net over F₉, using

t-expansion [i] based on digital (22, 115, 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]

(115−91, 115, 92)-Net over F₉ — Digital

Digital (24, 115, 92)-net over F₉, using

t-expansion [i] based on digital (23, 115, 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]

(115−91, 115, 548)-Net in Base 9 — Upper bound on s

There is no (24, 115, 549)-net in base 9, because

1 times m-reduction [i] would yield (24, 114, 549)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 145186 635344 428297 201585 751529 893620 785990 160359 548507 764932 087702 269714 954000 487010 417967 924931 021360 701577 > 9¹¹⁴ [i]