MinT - Best Known (26, 26+117, s)-Nets in Base 9

Best Known (26, 26+117, s)-Nets in Base 9

(26, 26+117, 78)-Net over F₉ — Constructive and digital

Digital (26, 143, 78)-net over F₉, using

t-expansion [i] based on digital (22, 143, 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]

(26, 26+117, 110)-Net over F₉ — Digital

Digital (26, 143, 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]

(26, 26+117, 573)-Net in Base 9 — Upper bound on s

There is no (26, 143, 574)-net in base 9, because

1 times m-reduction [i] would yield (26, 142, 574)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3327 724795 264645 201213 347672 106478 331271 348466 179692 018682 965759 526308 830756 734787 152653 701472 409218 818095 741332 161774 454066 891344 508321 > 9¹⁴² [i]