MinT - Best Known (115−55, 115, s)-Nets in Base 9

Best Known (115−55, 115, s)-Nets in Base 9

(115−55, 115, 232)-Net over F₉ — Constructive and digital

Digital (60, 115, 232)-net over F₉, using

1 times m-reduction [i] based on 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]

(115−55, 115, 268)-Net over F₉ — Digital

Digital (60, 115, 268)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−55, 115, 14583)-Net in Base 9 — Upper bound on s

There is no (60, 115, 14584)-net in base 9, because

1 times m-reduction [i] would yield (60, 114, 14584)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 085142 580886 891770 328997 699311 243597 465765 942062 322647 298461 264050 145394 058066 788027 805727 697993 998110 825025 > 9¹¹⁴ [i]