MinT - Best Known (58, 111, s)-Nets in Base 9

Best Known (58, 111, s)-Nets in Base 9

(58, 111, 232)-Net over F₉ — Constructive and digital

Digital (58, 111, 232)-net over F₉, using

1 times m-reduction [i] based on digital (58, 112, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 56, 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]

(58, 111, 262)-Net over F₉ — Digital

Digital (58, 111, 262)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 111, 14351)-Net in Base 9 — Upper bound on s

There is no (58, 111, 14352)-net in base 9, because

1 times m-reduction [i] would yield (58, 110, 14352)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 926 455207 492361 293379 697819 138487 528124 689234 420135 973183 881673 064366 305829 849075 734063 441435 496961 554177 > 9¹¹⁰ [i]