MinT - Best Known (238−68, 238, s)-Nets in Base 3

Best Known (238−68, 238, s)-Nets in Base 3

(238−68, 238, 288)-Net over F₃ — Constructive and digital

Digital (170, 238, 288)-net over F₃, using

3¹ times duplication [i] based on digital (169, 237, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 79, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(238−68, 238, 605)-Net over F₃ — Digital

Digital (170, 238, 605)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−68, 238, 14767)-Net in Base 3 — Upper bound on s

There is no (170, 238, 14768)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 359102 551239 476329 274268 169998 255507 626107 812082 430019 823903 786974 724170 372445 884761 153781 745208 961530 235234 263073 > 3²³⁸ [i]