MinT - Best Known (117−80, 117, s)-Nets in Base 9

Best Known (117−80, 117, s)-Nets in Base 9

(117−80, 117, 81)-Net over F₉ — Constructive and digital

Digital (37, 117, 81)-net over F₉, using

t-expansion [i] based on digital (32, 117, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(117−80, 117, 128)-Net over F₉ — Digital

Digital (37, 117, 128)-net over F₉, using

t-expansion [i] based on digital (33, 117, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(117−80, 117, 1194)-Net in Base 9 — Upper bound on s

There is no (37, 117, 1195)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4541 330134 126557 981401 025037 351220 915807 759998 944961 284493 375745 871162 867622 954436 276109 697813 614137 230926 425025 > 9¹¹⁷ [i]