MinT - Best Known (123−90, 123, s)-Nets in Base 9

Best Known (123−90, 123, s)-Nets in Base 9

(123−90, 123, 81)-Net over F₉ — Constructive and digital

Digital (33, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 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]

(123−90, 123, 128)-Net over F₉ — Digital

Digital (33, 123, 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]

(123−90, 123, 866)-Net in Base 9 — Upper bound on s

There is no (33, 123, 867)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2397 116888 306033 077232 527191 377710 577488 910301 427450 880709 493339 045394 742165 185139 408312 916854 960403 942161 179003 768889 > 9¹²³ [i]