MinT - Best Known (149−122, 149, s)-Nets in Base 9

Best Known (149−122, 149, s)-Nets in Base 9

(149−122, 149, 78)-Net over F₉ — Constructive and digital

Digital (27, 149, 78)-net over F₉, using

t-expansion [i] based on digital (22, 149, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(149−122, 149, 110)-Net over F₉ — Digital

Digital (27, 149, 110)-net over F₉, using

t-expansion [i] based on digital (26, 149, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(149−122, 149, 593)-Net in Base 9 — Upper bound on s

There is no (27, 149, 594)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15283 144241 075829 347376 619595 932781 653325 398419 981667 643395 768234 413073 316615 793701 970294 630647 860341 454760 617923 328266 732372 766168 762855 085265 > 9¹⁴⁹ [i]