MinT - Best Known (132, 175, s)-Nets in Base 4

Best Known (132, 175, s)-Nets in Base 4

(132, 175, 1028)-Net over F₄ — Constructive and digital

Digital (132, 175, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (132, 176, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 44, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(132, 175, 1796)-Net over F₄ — Digital

Digital (132, 175, 1796)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 175, 281735)-Net in Base 4 — Upper bound on s

There is no (132, 175, 281736)-net in base 4, because

1 times m-reduction [i] would yield (132, 174, 281736)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 379224 035455 139626 596892 900614 258778 320734 903472 069606 626512 104380 054056 064582 359117 462725 553180 680904 > 4¹⁷⁴ [i]