MinT - Best Known (37, 116, s)-Nets in Base 9

Best Known (37, 116, s)-Nets in Base 9

(37, 116, 81)-Net over F₉ — Constructive and digital

Digital (37, 116, 81)-net over F₉, using

t-expansion [i] based on digital (32, 116, 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]

(37, 116, 128)-Net over F₉ — Digital

Digital (37, 116, 128)-net over F₉, using

t-expansion [i] based on digital (33, 116, 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]

(37, 116, 1229)-Net in Base 9 — Upper bound on s

There is no (37, 116, 1230)-net in base 9, because

1 times m-reduction [i] would yield (37, 115, 1230)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55 086897 637725 934420 397611 160570 104091 384850 244550 333826 507983 494570 544222 275369 704237 452851 123143 894807 006801 > 9¹¹⁵ [i]