MinT - Best Known (127−66, 127, s)-Nets in Base 9

Best Known (127−66, 127, s)-Nets in Base 9

(127−66, 127, 128)-Net over F₉ — Constructive and digital

Digital (61, 127, 128)-net over F₉, using

4 times m-reduction [i] based on digital (61, 131, 128)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 48, 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, 83, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉ (see above)

(127−66, 127, 204)-Net over F₉ — Digital

Digital (61, 127, 204)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−66, 127, 7718)-Net in Base 9 — Upper bound on s

There is no (61, 127, 7719)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 491259 250542 197448 512125 473360 711145 162046 053053 740235 700799 260361 229245 373499 892455 311750 417220 550265 019070 664064 813113 > 9¹²⁷ [i]