MinT - Best Known (89, 89+61, s)-Nets in Base 9

Best Known (89, 89+61, s)-Nets in Base 9

(89, 89+61, 448)-Net over F₉ — Constructive and digital

Digital (89, 150, 448)-net over F₉, using

t-expansion [i] based on digital (88, 150, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 75, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(89, 89+61, 703)-Net over F₉ — Digital

Digital (89, 150, 703)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+61, 82605)-Net in Base 9 — Upper bound on s

There is no (89, 150, 82606)-net in base 9, because

1 times m-reduction [i] would yield (89, 149, 82606)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15214 765255 285391 767624 757089 181129 118527 055756 899799 202262 969649 009681 024424 737739 544567 723131 081207 759870 349361 833070 367340 850856 380691 818977 > 9¹⁴⁹ [i]