MinT - Best Known (32, 32+69, s)-Nets in Base 9

Best Known (32, 32+69, s)-Nets in Base 9

(32, 32+69, 81)-Net over F₉ — Constructive and digital

Digital (32, 101, 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]

(32, 32+69, 120)-Net over F₉ — Digital

Digital (32, 101, 120)-net over F₉, using

t-expansion [i] based on digital (31, 101, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(32, 32+69, 1063)-Net in Base 9 — Upper bound on s

There is no (32, 101, 1064)-net in base 9, because

1 times m-reduction [i] would yield (32, 100, 1064)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 271970 103994 237113 994166 935134 176117 639732 740284 260494 297182 786150 697630 611501 619619 738002 204545 > 9¹⁰⁰ [i]