MinT - Best Known (121−87, 121, s)-Nets in Base 9

Best Known (121−87, 121, s)-Nets in Base 9

(121−87, 121, 81)-Net over F₉ — Constructive and digital

Digital (34, 121, 81)-net over F₉, using

t-expansion [i] based on digital (32, 121, 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]

(121−87, 121, 128)-Net over F₉ — Digital

Digital (34, 121, 128)-net over F₉, using

t-expansion [i] based on digital (33, 121, 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]

(121−87, 121, 945)-Net in Base 9 — Upper bound on s

There is no (34, 121, 946)-net in base 9, because

1 times m-reduction [i] would yield (34, 120, 946)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 346481 322913 644457 063690 464668 250583 058473 943798 190530 836186 022641 220727 185689 343500 324777 078342 536269 884061 681265 > 9¹²⁰ [i]