MinT - Best Known (148−82, 148, s)-Nets in Base 9

Best Known (148−82, 148, s)-Nets in Base 9

(148−82, 148, 165)-Net over F₉ — Constructive and digital

Digital (66, 148, 165)-net over F₉, using

t-expansion [i] based on digital (64, 148, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(148−82, 148, 192)-Net over F₉ — Digital

Digital (66, 148, 192)-net over F₉, using

t-expansion [i] based on digital (61, 148, 192)-net over F₉, using
- net from sequence [i] based on digital (61, 191)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(148−82, 148, 5590)-Net in Base 9 — Upper bound on s

There is no (66, 148, 5591)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1694 585540 766220 413821 697019 310640 411229 341850 743304 805081 527950 315983 314097 728651 616958 156452 316305 706691 659299 521551 584952 551815 410287 099769 > 9¹⁴⁸ [i]