MinT - Best Known (149−112, 149, s)-Nets in Base 9

Best Known (149−112, 149, s)-Nets in Base 9

(149−112, 149, 81)-Net over F₉ — Constructive and digital

Digital (37, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(149−112, 149, 128)-Net over F₉ — Digital

Digital (37, 149, 128)-net over F₉, using

t-expansion [i] based on digital (33, 149, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(149−112, 149, 904)-Net in Base 9 — Upper bound on s

There is no (37, 149, 905)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15629 933434 772494 108990 245713 670149 517060 308677 970030 879662 460362 963710 838001 911763 896280 213110 710861 119023 440267 564604 864621 542040 497821 207745 > 9¹⁴⁹ [i]