MinT - Best Known (59, 59+55, s)-Nets in Base 9

Best Known (59, 59+55, s)-Nets in Base 9

(59, 59+55, 232)-Net over F₉ — Constructive and digital

Digital (59, 114, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 57, 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]

(59, 59+55, 256)-Net over F₉ — Digital

Digital (59, 114, 256)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+55, 13442)-Net in Base 9 — Upper bound on s

There is no (59, 114, 13443)-net in base 9, because

1 times m-reduction [i] would yield (59, 113, 13443)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 676260 194095 573717 065315 019716 063045 318804 613393 043408 121594 763723 884027 817800 858495 154545 025402 145916 948745 > 9¹¹³ [i]