MinT - Best Known (121, 121+48, s)-Nets in Base 3

Best Known (121, 121+48, s)-Nets in Base 3

(121, 121+48, 252)-Net over F₃ — Constructive and digital

Digital (121, 169, 252)-net over F₃, using

3¹ times duplication [i] based on digital (120, 168, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 56, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(121, 121+48, 461)-Net over F₃ — Digital

Digital (121, 169, 461)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+48, 11198)-Net in Base 3 — Upper bound on s

There is no (121, 169, 11199)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430 671241 121842 473690 439618 430959 606659 205982 145850 852876 610382 415501 280856 949713 > 3¹⁶⁹ [i]