MinT - Best Known (116−42, 116, s)-Nets in Base 9

Best Known (116−42, 116, s)-Nets in Base 9

(116−42, 116, 740)-Net over F₉ — Constructive and digital

Digital (74, 116, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 58, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(116−42, 116, 1031)-Net over F₉ — Digital

Digital (74, 116, 1031)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−42, 116, 202502)-Net in Base 9 — Upper bound on s

There is no (74, 116, 202503)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 237927 902964 679389 147274 479942 524326 702481 267315 382528 115731 428280 056452 242424 349693 863530 129256 637515 172505 > 9¹¹⁶ [i]