MinT - Best Known (177, 177+60, s)-Nets in Base 3

Best Known (177, 177+60, s)-Nets in Base 3

(177, 177+60, 324)-Net over F₃ — Constructive and digital

Digital (177, 237, 324)-net over F₃, using

t-expansion [i] based on digital (176, 237, 324)-net over F₃, using
- trace code for nets [i] based on digital (18, 79, 108)-net over F₂₇, using
  - net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
      - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(177, 177+60, 931)-Net over F₃ — Digital

Digital (177, 237, 931)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+60, 35371)-Net in Base 3 — Upper bound on s

There is no (177, 237, 35372)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119642 625276 490500 889131 918903 922262 356452 653620 233241 865596 789704 869337 485594 781570 123010 082254 454530 246760 423241 > 3²³⁷ [i]