MinT - Best Known (148−113, 148, s)-Nets in Base 9

Best Known (148−113, 148, s)-Nets in Base 9

(148−113, 148, 81)-Net over F₉ — Constructive and digital

Digital (35, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(148−113, 148, 128)-Net over F₉ — Digital

Digital (35, 148, 128)-net over F₉, using

t-expansion [i] based on digital (33, 148, 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]

(148−113, 148, 833)-Net in Base 9 — Upper bound on s

There is no (35, 148, 834)-net in base 9, because

1 times m-reduction [i] would yield (35, 147, 834)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 191 096883 543992 306617 663960 469287 238185 027821 661661 560149 430531 371214 604729 087378 371267 115896 147606 456135 412114 576539 295352 275755 748878 235265 > 9¹⁴⁷ [i]