MinT - Best Known (165−48, 165, s)-Nets in Base 3

Best Known (165−48, 165, s)-Nets in Base 3

(165−48, 165, 246)-Net over F₃ — Constructive and digital

Digital (117, 165, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 55, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(165−48, 165, 416)-Net over F₃ — Digital

Digital (117, 165, 416)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−48, 165, 9320)-Net in Base 3 — Upper bound on s

There is no (117, 165, 9321)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 312908 498256 507011 830734 372177 542684 893417 069065 809246 162973 427357 652103 276001 > 3¹⁶⁵ [i]