MinT - Best Known (68, 115, s)-Nets in Base 9

Best Known (68, 115, s)-Nets in Base 9

(68, 115, 344)-Net over F₉ — Constructive and digital

Digital (68, 115, 344)-net over F₉, using

7 times m-reduction [i] based on digital (68, 122, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 61, 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]

(68, 115, 553)-Net over F₉ — Digital

Digital (68, 115, 553)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 115, 63240)-Net in Base 9 — Upper bound on s

There is no (68, 115, 63241)-net in base 9, because

1 times m-reduction [i] would yield (68, 114, 63241)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 077670 779436 632129 987137 173091 624265 844253 305051 376264 139169 438059 042397 209109 911575 135221 992502 210191 674041 > 9¹¹⁴ [i]