MinT - Best Known (120, 120+52, s)-Nets in Base 3

Best Known (120, 120+52, s)-Nets in Base 3

(120, 120+52, 204)-Net over F₃ — Constructive and digital

Digital (120, 172, 204)-net over F₃, using

3¹ times duplication [i] based on digital (119, 171, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 57, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(120, 120+52, 380)-Net over F₃ — Digital

Digital (120, 172, 380)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+52, 7535)-Net in Base 3 — Upper bound on s

There is no (120, 172, 7536)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11612 190135 665743 484233 186363 506350 366058 494558 169887 999025 523546 405765 917972 669345 > 3¹⁷² [i]