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

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

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

Digital (26, 117, 78)-net over F₉, using

t-expansion [i] based on digital (22, 117, 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, 117, 110)-Net over F₉ — Digital

Digital (26, 117, 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, 117, 607)-Net in Base 9 — Upper bound on s

There is no (26, 117, 608)-net in base 9, because

1 times m-reduction [i] would yield (26, 116, 608)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 495 041637 543366 907725 282294 362261 644387 273960 588706 450432 973178 685254 139583 089517 986356 875788 175133 907002 343169 > 9¹¹⁶ [i]