MinT - Best Known (142, 142+46, s)-Nets in Base 3

Best Known (142, 142+46, s)-Nets in Base 3

(142, 142+46, 400)-Net over F₃ — Constructive and digital

Digital (142, 188, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 47, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(142, 142+46, 881)-Net over F₃ — Digital

Digital (142, 188, 881)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+46, 37420)-Net in Base 3 — Upper bound on s

There is no (142, 188, 37421)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 499864 185235 976203 370852 303559 641685 298314 600490 197378 376505 225198 920423 555478 737172 779707 > 3¹⁸⁸ [i]