MinT - Best Known (50, 50+97, s)-Nets in Base 9

Best Known (50, 50+97, s)-Nets in Base 9

(50, 50+97, 81)-Net over F₉ — Constructive and digital

Digital (50, 147, 81)-net over F₉, using

t-expansion [i] based on digital (32, 147, 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]

(50, 50+97, 182)-Net over F₉ — Digital

Digital (50, 147, 182)-net over F₉, using

net from sequence [i] based on digital (50, 181)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
  - a curve from the manYPoints database [i]

(50, 50+97, 1842)-Net in Base 9 — Upper bound on s

There is no (50, 147, 1843)-net in base 9, because

1 times m-reduction [i] would yield (50, 146, 1843)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 338014 633089 520632 743535 644449 797363 632701 611573 033237 613052 907777 086497 211406 228529 451155 306901 200897 641754 065354 887486 989710 850682 812545 > 9¹⁴⁶ [i]