MinT - Best Known (141−45, 141, s)-Nets in Base 9

Best Known (141−45, 141, s)-Nets in Base 9

(141−45, 141, 740)-Net over F₉ — Constructive and digital

Digital (96, 141, 740)-net over F₉, using

t-expansion [i] based on digital (91, 141, 740)-net over F₉, using
- 9 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]

(141−45, 141, 2487)-Net over F₉ — Digital

Digital (96, 141, 2487)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−45, 141, 1337245)-Net in Base 9 — Upper bound on s

There is no (96, 141, 1337246)-net in base 9, because

1 times m-reduction [i] would yield (96, 140, 1337246)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 260565 918110 219938 339225 558113 119206 362944 935463 077588 402258 398281 767548 999117 774364 801336 710503 819545 434506 251284 844987 553456 321121 > 9¹⁴⁰ [i]