MinT - Best Known (142, 142+41, s)-Nets in Base 3

Best Known (142, 142+41, s)-Nets in Base 3

(142, 142+41, 600)-Net over F₃ — Constructive and digital

Digital (142, 183, 600)-net over F₃, using

1 times m-reduction [i] based on digital (142, 184, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 46, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(142, 142+41, 1221)-Net over F₃ — Digital

Digital (142, 183, 1221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+41, 91198)-Net in Base 3 — Upper bound on s

There is no (142, 183, 91199)-net in base 3, because

1 times m-reduction [i] would yield (142, 182, 91199)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 685 699224 877552 067808 136360 346962 989686 526088 677113 759292 771577 386992 641736 637365 022681 > 3¹⁸² [i]