MinT - Best Known (91, 91+55, s)-Nets in Base 9

Best Known (91, 91+55, s)-Nets in Base 9

(91, 91+55, 740)-Net over F₉ — Constructive and digital

Digital (91, 146, 740)-net over F₉, using

4 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 75, 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]

(91, 91+55, 1021)-Net over F₉ — Digital

Digital (91, 146, 1021)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+55, 181933)-Net in Base 9 — Upper bound on s

There is no (91, 146, 181934)-net in base 9, because

1 times m-reduction [i] would yield (91, 145, 181934)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 318337 257482 566507 495567 001645 202130 259495 738790 152437 586254 488398 095748 016943 850806 524118 778449 180569 962474 705037 701209 075355 803170 094225 > 9¹⁴⁵ [i]