MinT - Best Known (59, 59+64, s)-Nets in Base 9

Best Known (59, 59+64, s)-Nets in Base 9

(59, 59+64, 128)-Net over F₉ — Constructive and digital

Digital (59, 123, 128)-net over F₉, using

2 times m-reduction [i] based on digital (59, 125, 128)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 46, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
        a function field by GarcÃa and Quoos [i]
  2. digital (13, 79, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉ (see above)

(59, 59+64, 198)-Net over F₉ — Digital

Digital (59, 123, 198)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+64, 7422)-Net in Base 9 — Upper bound on s

There is no (59, 123, 7423)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2364 191532 124097 314891 207584 898915 793942 263599 089323 730560 419681 524620 495644 642480 657320 215097 273308 858739 610164 330241 > 9¹²³ [i]