MinT - Best Known (133−42, 133, s)-Nets in Base 3

Best Known (133−42, 133, s)-Nets in Base 3

(133−42, 133, 156)-Net over F₃ — Constructive and digital

Digital (91, 133, 156)-net over F₃, using

5 times m-reduction [i] based on digital (91, 138, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 69, 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]

(133−42, 133, 267)-Net over F₃ — Digital

Digital (91, 133, 267)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−42, 133, 4542)-Net in Base 3 — Upper bound on s

There is no (91, 133, 4543)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2873 878054 289761 216262 800206 390197 870492 749273 949514 757315 478871 > 3¹³³ [i]