MinT - Best Known (116−56, 116, s)-Nets in Base 9

Best Known (116−56, 116, s)-Nets in Base 9

(116−56, 116, 232)-Net over F₉ — Constructive and digital

Digital (60, 116, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 58, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(116−56, 116, 259)-Net over F₉ — Digital

Digital (60, 116, 259)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−56, 116, 12665)-Net in Base 9 — Upper bound on s

There is no (60, 116, 12666)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 706306 164216 258178 139649 247204 956024 854474 601613 543855 251481 304134 076886 672015 706767 696745 240660 446057 243713 > 9¹¹⁶ [i]