MinT - Best Known (121−97, 121, s)-Nets in Base 9

Best Known (121−97, 121, s)-Nets in Base 9

(121−97, 121, 78)-Net over F₉ — Constructive and digital

Digital (24, 121, 78)-net over F₉, using

t-expansion [i] based on digital (22, 121, 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]

(121−97, 121, 92)-Net over F₉ — Digital

Digital (24, 121, 92)-net over F₉, using

t-expansion [i] based on digital (23, 121, 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]

(121−97, 121, 540)-Net in Base 9 — Upper bound on s

There is no (24, 121, 541)-net in base 9, because

1 times m-reduction [i] would yield (24, 120, 541)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 456877 922368 547909 863541 715491 030682 935074 177828 998657 153438 972614 501898 020891 898683 163759 076128 885282 405660 834177 > 9¹²⁰ [i]