MinT - Best Known (131, 131+37, s)-Nets in Base 3

Best Known (131, 131+37, s)-Nets in Base 3

(131, 131+37, 640)-Net over F₃ — Constructive and digital

Digital (131, 168, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 42, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(131, 131+37, 1221)-Net over F₃ — Digital

Digital (131, 168, 1221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+37, 100843)-Net in Base 3 — Upper bound on s

There is no (131, 168, 100844)-net in base 3, because

1 times m-reduction [i] would yield (131, 167, 100844)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 781129 386621 801702 936768 621195 037803 218742 146618 150728 044132 781872 602584 773545 > 3¹⁶⁷ [i]