MinT - Best Known (59, 59+61, s)-Nets in Base 9

Best Known (59, 59+61, s)-Nets in Base 9

(59, 59+61, 128)-Net over F₉ — Constructive and digital

Digital (59, 120, 128)-net over F₉, using

5 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+61, 214)-Net over F₉ — Digital

Digital (59, 120, 214)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+61, 9162)-Net in Base 9 — Upper bound on s

There is no (59, 120, 9163)-net in base 9, because

1 times m-reduction [i] would yield (59, 119, 9163)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 359814 529476 338372 370028 039800 784415 401264 429335 303661 760208 451605 201400 243575 707382 577736 038492 144175 188750 979025 > 9¹¹⁹ [i]