MinT - Best Known (121, 121+44, s)-Nets in Base 3

Best Known (121, 121+44, s)-Nets in Base 3

(121, 121+44, 288)-Net over F₃ — Constructive and digital

Digital (121, 165, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 55, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(121, 121+44, 567)-Net over F₃ — Digital

Digital (121, 165, 567)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+44, 17127)-Net in Base 3 — Upper bound on s

There is no (121, 165, 17128)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 313971 373071 304455 297643 081107 896011 761262 216233 439231 824113 246665 639914 282097 > 3¹⁶⁵ [i]