MinT - Best Known (129, 129+58, s)-Nets in Base 3

Best Known (129, 129+58, s)-Nets in Base 3

(129, 129+58, 192)-Net over F₃ — Constructive and digital

Digital (129, 187, 192)-net over F₃, using

3¹ times duplication [i] based on digital (128, 186, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 62, 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]

(129, 129+58, 376)-Net over F₃ — Digital

Digital (129, 187, 376)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+58, 6933)-Net in Base 3 — Upper bound on s

There is no (129, 187, 6934)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 167276 175095 412996 221981 021042 156303 350597 923840 799579 877232 130454 866894 606053 589592 139861 > 3¹⁸⁷ [i]