MinT - Best Known (89, 128, s)-Nets in Base 9

Best Known (89, 128, s)-Nets in Base 9

(89, 128, 740)-Net over F₉ — Constructive and digital

Digital (89, 128, 740)-net over F₉, using

18 times m-reduction [i] based on digital (89, 146, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 73, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(89, 128, 3095)-Net over F₉ — Digital

Digital (89, 128, 3095)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 128, 2368542)-Net in Base 9 — Upper bound on s

There is no (89, 128, 2368543)-net in base 9, because

1 times m-reduction [i] would yield (89, 127, 2368543)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 445392 822139 145159 894298 137029 394177 638897 052272 708772 065306 938158 101642 957938 404218 806578 036032 690395 954031 144178 837097 > 9¹²⁷ [i]