MinT - Best Known (122−102, 122, s)-Nets in Base 9

Best Known (122−102, 122, s)-Nets in Base 9

(122−102, 122, 74)-Net over F₉ — Constructive and digital

Digital (20, 122, 74)-net over F₉, using

t-expansion [i] based on digital (17, 122, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(122−102, 122, 84)-Net over F₉ — Digital

Digital (20, 122, 84)-net over F₉, using

t-expansion [i] based on digital (19, 122, 84)-net over F₉, using
- net from sequence [i] based on digital (19, 83)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
    - Drinfeld modules of rank 1 [i]

(122−102, 122, 444)-Net in Base 9 — Upper bound on s

There is no (20, 122, 445)-net in base 9, because

2 times m-reduction [i] would yield (20, 120, 445)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 269332 578566 845889 341263 307566 913317 056206 186358 792073 947872 396474 671369 845105 659665 832926 589065 085608 692945 737233 > 9¹²⁰ [i]