MinT - Best Known (91, 91+59, s)-Nets in Base 9

Best Known (91, 91+59, s)-Nets in Base 9

(91, 91+59, 740)-Net over F₉ — Constructive and digital

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+59, 831)-Net over F₉ — Digital

Digital (91, 150, 831)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+59, 116626)-Net in Base 9 — Upper bound on s

There is no (91, 150, 116627)-net in base 9, because

1 times m-reduction [i] would yield (91, 149, 116627)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15210 655257 332169 232349 236340 503110 383206 457525 314492 772886 821102 154746 383395 421312 324309 623176 113962 064184 759756 206083 367801 181778 456634 243641 > 9¹⁴⁹ [i]