MinT - Best Known (137−105, 137, s)-Nets in Base 9

Best Known (137−105, 137, s)-Nets in Base 9

(137−105, 137, 81)-Net over F₉ — Constructive and digital

Digital (32, 137, 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]

(137−105, 137, 120)-Net over F₉ — Digital

Digital (32, 137, 120)-net over F₉, using

t-expansion [i] based on digital (31, 137, 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]

(137−105, 137, 759)-Net in Base 9 — Upper bound on s

There is no (32, 137, 760)-net in base 9, because

1 times m-reduction [i] would yield (32, 136, 760)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 5985 979340 710446 002017 377033 395808 454582 255766 563678 901604 366043 500531 091148 945878 467023 496158 245707 340932 454925 652453 356640 892161 > 9¹³⁶ [i]