MinT - Best Known (89, 144, s)-Nets in Base 9

Best Known (89, 144, s)-Nets in Base 9

(89, 144, 740)-Net over F₉ — Constructive and digital

Digital (89, 144, 740)-net over F₉, using

2 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, 144, 938)-Net over F₉ — Digital

Digital (89, 144, 938)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 144, 154604)-Net in Base 9 — Upper bound on s

There is no (89, 144, 154605)-net in base 9, because

1 times m-reduction [i] would yield (89, 143, 154605)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28623 593505 054845 456239 927763 701275 529282 352614 195217 153790 551255 781059 580512 604487 006389 022590 620313 428573 225482 433871 135789 842488 755001 > 9¹⁴³ [i]