MinT - Best Known (129−42, 129, s)-Nets in Base 4

Best Known (129−42, 129, s)-Nets in Base 4

(129−42, 129, 240)-Net over F₄ — Constructive and digital

Digital (87, 129, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 43, 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]

(129−42, 129, 417)-Net over F₄ — Digital

Digital (87, 129, 417)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−42, 129, 14428)-Net in Base 4 — Upper bound on s

There is no (87, 129, 14429)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 463337 425644 644440 092063 772450 243521 851450 853317 075967 958675 268343 568485 233788 > 4¹²⁹ [i]