MinT - Best Known (164−76, 164, s)-Nets in Base 4

Best Known (164−76, 164, s)-Nets in Base 4

(164−76, 164, 130)-Net over F₄ — Constructive and digital

Digital (88, 164, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 82, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(164−76, 164, 154)-Net over F₄ — Digital

Digital (88, 164, 154)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−76, 164, 1955)-Net in Base 4 — Upper bound on s

There is no (88, 164, 1956)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 553 918710 119690 385522 581238 559010 246037 375246 237408 230504 618918 007763 308278 169785 363539 429415 850400 > 4¹⁶⁴ [i]