MinT - Best Known (131, 131+64, s)-Nets in Base 4

Best Known (131, 131+64, s)-Nets in Base 4

(131, 131+64, 240)-Net over F₄ — Constructive and digital

Digital (131, 195, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 65, 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]

(131, 131+64, 570)-Net over F₄ — Digital

Digital (131, 195, 570)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+64, 19860)-Net in Base 4 — Upper bound on s

There is no (131, 195, 19861)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2523 669014 299893 535892 054045 202858 072017 408309 643593 522473 440938 782875 262311 665291 614675 167685 573504 254144 518131 564060 > 4¹⁹⁵ [i]