MinT - Best Known (226−70, 226, s)-Nets in Base 3

Best Known (226−70, 226, s)-Nets in Base 3

(226−70, 226, 204)-Net over F₃ — Constructive and digital

Digital (156, 226, 204)-net over F₃, using

3¹ times duplication [i] based on digital (155, 225, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 75, 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]

(226−70, 226, 446)-Net over F₃ — Digital

Digital (156, 226, 446)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−70, 226, 8342)-Net in Base 3 — Upper bound on s

There is no (156, 226, 8343)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 677197 012654 558471 749880 207761 685837 023776 550135 551271 157720 327349 274596 232815 672103 867544 483064 371287 214363 > 3²²⁶ [i]