MinT - Best Known (118, 168, s)-Nets in Base 3

Best Known (118, 168, s)-Nets in Base 3

(118, 168, 228)-Net over F₃ — Constructive and digital

Digital (118, 168, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 56, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(118, 168, 392)-Net over F₃ — Digital

Digital (118, 168, 392)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 168, 8157)-Net in Base 3 — Upper bound on s

There is no (118, 168, 8158)-net in base 3, because

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]