MinT - Best Known (114−94, 114, s)-Nets in Base 9

Best Known (114−94, 114, s)-Nets in Base 9

(114−94, 114, 74)-Net over F₉ — Constructive and digital

Digital (20, 114, 74)-net over F₉, using

t-expansion [i] based on digital (17, 114, 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]

(114−94, 114, 84)-Net over F₉ — Digital

Digital (20, 114, 84)-net over F₉, using

t-expansion [i] based on digital (19, 114, 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]

(114−94, 114, 445)-Net in Base 9 — Upper bound on s

There is no (20, 114, 446)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 459274 957681 400380 612736 301677 113418 965718 486132 726561 093420 585667 998300 199138 320242 307469 210352 779510 330705 > 9¹¹⁴ [i]