MinT - Best Known (126−56, 126, s)-Nets in Base 9

Best Known (126−56, 126, s)-Nets in Base 9

(126−56, 126, 344)-Net over F₉ — Constructive and digital

Digital (70, 126, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 63, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(126−56, 126, 398)-Net over F₉ — Digital

Digital (70, 126, 398)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−56, 126, 27780)-Net in Base 9 — Upper bound on s

There is no (70, 126, 27781)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716946 964666 757297 741676 264630 579945 704539 599055 285662 117216 328045 692488 334684 453954 644464 693806 748647 857069 478374 229473 > 9¹²⁶ [i]