MinT - Best Known (133−90, 133, s)-Nets in Base 9

Best Known (133−90, 133, s)-Nets in Base 9

(133−90, 133, 81)-Net over F₉ — Constructive and digital

Digital (43, 133, 81)-net over F₉, using

t-expansion [i] based on digital (32, 133, 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]

(133−90, 133, 147)-Net over F₉ — Digital

Digital (43, 133, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(133−90, 133, 1429)-Net in Base 9 — Upper bound on s

There is no (43, 133, 1430)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 380265 994672 764774 254081 658297 729031 854374 279813 035465 196810 518689 059780 021297 585440 997329 979045 680365 176774 204299 438495 224945 > 9¹³³ [i]