MinT - Best Known (62, 123, s)-Nets in Base 9

Best Known (62, 123, s)-Nets in Base 9

(62, 123, 164)-Net over F₉ — Constructive and digital

Digital (62, 123, 164)-net over F₉, using

1 times m-reduction [i] based on digital (62, 124, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 62, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(62, 123, 243)-Net over F₉ — Digital

Digital (62, 123, 243)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 123, 11418)-Net in Base 9 — Upper bound on s

There is no (62, 123, 11419)-net in base 9, because

1 times m-reduction [i] would yield (62, 122, 11419)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 262 227444 877624 530274 460664 907771 452117 552047 714266 495749 141021 079016 050080 651069 938143 127677 222612 201520 395735 995601 > 9¹²² [i]