MinT - Best Known (146−103, 146, s)-Nets in Base 9

Best Known (146−103, 146, s)-Nets in Base 9

(146−103, 146, 81)-Net over F₉ — Constructive and digital

Digital (43, 146, 81)-net over F₉, using

t-expansion [i] based on digital (32, 146, 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]

(146−103, 146, 147)-Net over F₉ — Digital

Digital (43, 146, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(146−103, 146, 1250)-Net in Base 9 — Upper bound on s

There is no (43, 146, 1251)-net in base 9, because

1 times m-reduction [i] would yield (43, 145, 1251)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 354366 750368 985301 904701 598104 135138 741604 382601 812720 590012 377317 876870 336102 883582 721630 802313 329812 242298 169313 076641 363525 269324 366409 > 9¹⁴⁵ [i]