MinT - Best Known (169−51, 169, s)-Nets in Base 3

Best Known (169−51, 169, s)-Nets in Base 3

(169−51, 169, 204)-Net over F₃ — Constructive and digital

Digital (118, 169, 204)-net over F₃, using

3¹ times duplication [i] based on digital (117, 168, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 56, 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]

(169−51, 169, 376)-Net over F₃ — Digital

Digital (118, 169, 376)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−51, 169, 8157)-Net in Base 3 — Upper bound on s

There is no (118, 169, 8158)-net in base 3, because

1 times m-reduction [i] would yield (118, 168, 8158)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 619670 911060 592648 924769 344219 634949 578957 744012 907103 532756 574715 419854 431245 > 3¹⁶⁸ [i]