MinT - Best Known (90, 90+58, s)-Nets in Base 9

Best Known (90, 90+58, s)-Nets in Base 9

(90, 90+58, 740)-Net over F₉ — Constructive and digital

Digital (90, 148, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 74, 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]

(90, 90+58, 838)-Net over F₉ — Digital

Digital (90, 148, 838)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+58, 108115)-Net in Base 9 — Upper bound on s

There is no (90, 148, 108116)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1690 179415 512860 049753 553034 404605 994265 831434 633220 940895 459761 441840 102671 315143 348868 693974 433860 593562 140612 218367 738551 258708 867865 308961 > 9¹⁴⁸ [i]