MinT - Best Known (128−40, 128, s)-Nets in Base 4

Best Known (128−40, 128, s)-Nets in Base 4

(128−40, 128, 240)-Net over F₄ — Constructive and digital

Digital (88, 128, 240)-net over F₄, using

t-expansion [i] based on digital (87, 128, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (87, 129, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 43, 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]

(128−40, 128, 489)-Net over F₄ — Digital

Digital (88, 128, 489)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−40, 128, 19724)-Net in Base 4 — Upper bound on s

There is no (88, 128, 19725)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115812 257635 076118 252957 601468 775392 976868 013200 656172 509807 626197 752703 879856 > 4¹²⁸ [i]