MinT - Best Known (33, 33+99, s)-Nets in Base 9

Best Known (33, 33+99, s)-Nets in Base 9

(33, 33+99, 81)-Net over F₉ — Constructive and digital

Digital (33, 132, 81)-net over F₉, using

t-expansion [i] based on digital (32, 132, 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]

(33, 33+99, 128)-Net over F₉ — Digital

Digital (33, 132, 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]

(33, 33+99, 820)-Net in Base 9 — Upper bound on s

There is no (33, 132, 821)-net in base 9, because

1 times m-reduction [i] would yield (33, 131, 821)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106976 176481 665415 720290 394106 109090 942920 644270 661152 186109 148626 176952 731029 018421 027967 056435 380814 302973 406825 008321 930025 > 9¹³¹ [i]