MinT - Best Known (238−56, 238, s)-Nets in Base 3

Best Known (238−56, 238, s)-Nets in Base 3

(238−56, 238, 464)-Net over F₃ — Constructive and digital

Digital (182, 238, 464)-net over F₃, using

2 times m-reduction [i] based on digital (182, 240, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 60, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(238−56, 238, 1254)-Net over F₃ — Digital

Digital (182, 238, 1254)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−56, 238, 64168)-Net in Base 3 — Upper bound on s

There is no (182, 238, 64169)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 358935 116617 985115 254384 327989 511717 980578 393317 997236 649478 256410 494997 370082 599281 829370 887236 952825 055837 258225 > 3²³⁸ [i]