MinT - Best Known (138−44, 138, s)-Nets in Base 3

Best Known (138−44, 138, s)-Nets in Base 3

(138−44, 138, 156)-Net over F₃ — Constructive and digital

Digital (94, 138, 156)-net over F₃, using

6 times m-reduction [i] based on digital (94, 144, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 72, 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]

(138−44, 138, 267)-Net over F₃ — Digital

Digital (94, 138, 267)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−44, 138, 4431)-Net in Base 3 — Upper bound on s

There is no (94, 138, 4432)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696999 475476 323263 338530 064220 686675 469270 790839 843291 215792 114657 > 3¹³⁸ [i]