MinT - Best Known (102, 135, s)-Nets in Base 4

Best Known (102, 135, s)-Nets in Base 4

(102, 135, 1028)-Net over F₄ — Constructive and digital

Digital (102, 135, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (102, 136, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 34, 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]

(102, 135, 1494)-Net over F₄ — Digital

Digital (102, 135, 1494)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 135, 249831)-Net in Base 4 — Upper bound on s

There is no (102, 135, 249832)-net in base 4, because

1 times m-reduction [i] would yield (102, 134, 249832)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 474 292700 364566 126892 374584 819795 206283 650847 926352 636217 150773 538081 947928 460946 > 4¹³⁴ [i]