MinT - Best Known (159−52, 159, s)-Nets in Base 4

Best Known (159−52, 159, s)-Nets in Base 4

(159−52, 159, 240)-Net over F₄ — Constructive and digital

Digital (107, 159, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 53, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(159−52, 159, 486)-Net over F₄ — Digital

Digital (107, 159, 486)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−52, 159, 16883)-Net in Base 4 — Upper bound on s

There is no (107, 159, 16884)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534604 559863 237553 353556 004361 868687 713925 677051 556887 765388 949451 194656 537082 510796 256719 574092 > 4¹⁵⁹ [i]