MinT - Best Known (137, 137+62, s)-Nets in Base 3

Best Known (137, 137+62, s)-Nets in Base 3

(137, 137+62, 192)-Net over F₃ — Constructive and digital

Digital (137, 199, 192)-net over F₃, using

3¹ times duplication [i] based on digital (136, 198, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 66, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(137, 137+62, 392)-Net over F₃ — Digital

Digital (137, 199, 392)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+62, 7144)-Net in Base 3 — Upper bound on s

There is no (137, 199, 7145)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88761 354573 412865 305019 065885 198033 635424 867641 257684 601325 253770 203577 579043 794407 179398 184907 > 3¹⁹⁹ [i]