MinT - Best Known (114−93, 114, s)-Nets in Base 9

Best Known (114−93, 114, s)-Nets in Base 9

(114−93, 114, 74)-Net over F₉ — Constructive and digital

Digital (21, 114, 74)-net over F₉, using

t-expansion [i] based on digital (17, 114, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(114−93, 114, 88)-Net over F₉ — Digital

Digital (21, 114, 88)-net over F₉, using

net from sequence [i] based on digital (21, 87)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
  - a curve from the manYPoints database [i]

(114−93, 114, 469)-Net in Base 9 — Upper bound on s

There is no (21, 114, 470)-net in base 9, because

1 times m-reduction [i] would yield (21, 113, 470)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 734052 202116 109787 648695 477858 530954 607075 614311 317140 774129 470252 935219 888197 217060 692093 648248 387304 293217 > 9¹¹³ [i]