MinT - Best Known (177−48, 177, s)-Nets in Base 3

Best Known (177−48, 177, s)-Nets in Base 3

(177−48, 177, 288)-Net over F₃ — Constructive and digital

Digital (129, 177, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 59, 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]

(177−48, 177, 564)-Net over F₃ — Digital

Digital (129, 177, 564)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−48, 177, 16161)-Net in Base 3 — Upper bound on s

There is no (129, 177, 16162)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 825087 649601 303384 272945 020140 107340 265261 646769 598435 790700 200712 637537 723871 168753 > 3¹⁷⁷ [i]