MinT - Best Known (38, 38+65, s)-Nets in Base 9

Best Known (38, 38+65, s)-Nets in Base 9

(38, 38+65, 81)-Net over F₉ — Constructive and digital

Digital (38, 103, 81)-net over F₉, using

t-expansion [i] based on digital (32, 103, 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]

(38, 38+65, 128)-Net over F₉ — Digital

Digital (38, 103, 128)-net over F₉, using

t-expansion [i] based on digital (33, 103, 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]

(38, 38+65, 1740)-Net in Base 9 — Upper bound on s

There is no (38, 103, 1741)-net in base 9, because

1 times m-reduction [i] would yield (38, 102, 1741)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 805149 281606 460010 946881 105286 065168 530332 957193 745216 516618 178347 338319 952621 479169 639322 198273 > 9¹⁰² [i]