MinT - Best Known (82, 132, s)-Nets in Base 9

Best Known (82, 132, s)-Nets in Base 9

(82, 132, 740)-Net over F₉ — Constructive and digital

Digital (82, 132, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 66, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(82, 132, 913)-Net over F₉ — Digital

Digital (82, 132, 913)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 132, 138959)-Net in Base 9 — Upper bound on s

There is no (82, 132, 138960)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912075 502138 719598 655097 359659 886657 409435 228698 252090 314406 205326 758853 974967 265208 244802 311861 984860 960371 763339 943121 652353 > 9¹³² [i]