MinT - Best Known (207−62, 207, s)-Nets in Base 4

Best Known (207−62, 207, s)-Nets in Base 4

(207−62, 207, 531)-Net over F₄ — Constructive and digital

Digital (145, 207, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 69, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(207−62, 207, 860)-Net over F₄ — Digital

Digital (145, 207, 860)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−62, 207, 43337)-Net in Base 4 — Upper bound on s

There is no (145, 207, 43338)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42319 233212 490372 429995 424595 798348 920044 466284 421337 873561 915570 424986 612936 498598 073158 320821 833485 626198 405992 479948 913440 > 4²⁰⁷ [i]