MinT - Best Known (49, 49+100, s)-Nets in Base 9

Best Known (49, 49+100, s)-Nets in Base 9

(49, 49+100, 81)-Net over F₉ — Constructive and digital

Digital (49, 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]

(49, 49+100, 168)-Net over F₉ — Digital

Digital (49, 149, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(49, 49+100, 1668)-Net in Base 9 — Upper bound on s

There is no (49, 149, 1669)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15438 828053 162432 771693 220401 114535 938637 184750 856185 454196 539653 664738 015173 876448 208560 833686 819716 113625 990325 240672 900038 423102 504957 538705 > 9¹⁴⁹ [i]