MinT - Best Known (125−87, 125, s)-Nets in Base 9

Best Known (125−87, 125, s)-Nets in Base 9

(125−87, 125, 81)-Net over F₉ — Constructive and digital

Digital (38, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 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]

(125−87, 125, 128)-Net over F₉ — Digital

Digital (38, 125, 128)-net over F₉, using

t-expansion [i] based on digital (33, 125, 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]

(125−87, 125, 1165)-Net in Base 9 — Upper bound on s

There is no (38, 125, 1166)-net in base 9, because

1 times m-reduction [i] would yield (38, 124, 1166)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21618 192755 115145 254361 688539 269021 923313 140034 105711 242263 870882 426691 239619 629839 471360 392002 121510 963166 922183 886481 > 9¹²⁴ [i]