MinT - Best Known (165−50, 165, s)-Nets in Base 4

Best Known (165−50, 165, s)-Nets in Base 4

(165−50, 165, 384)-Net over F₄ — Constructive and digital

Digital (115, 165, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 55, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(165−50, 165, 679)-Net over F₄ — Digital

Digital (115, 165, 679)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−50, 165, 31902)-Net in Base 4 — Upper bound on s

There is no (115, 165, 31903)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2188 214087 823413 558067 339807 502536 446096 467890 552010 092574 624096 673188 105867 246094 444509 582042 355242 > 4¹⁶⁵ [i]