MinT - Best Known (229−68, 229, s)-Nets in Base 3

Best Known (229−68, 229, s)-Nets in Base 3

(229−68, 229, 252)-Net over F₃ — Constructive and digital

Digital (161, 229, 252)-net over F₃, using

3¹ times duplication [i] based on digital (160, 228, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 76, 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]

(229−68, 229, 515)-Net over F₃ — Digital

Digital (161, 229, 515)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−68, 229, 11032)-Net in Base 3 — Upper bound on s

There is no (161, 229, 11033)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 245199 528519 348778 307884 194907 831443 408218 263688 018501 021316 516599 436220 539972 007697 945141 032180 564811 763705 > 3²²⁹ [i]