MinT - Best Known (128, 128+32, s)-Nets in Base 4

Best Known (128, 128+32, s)-Nets in Base 4

(128, 128+32, 1062)-Net over F₄ — Constructive and digital

Digital (128, 160, 1062)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (16, 32, 34)-net over F₄, using
  - trace code for nets [i] based on digital (0, 16, 17)-net over F₁₆, using
    - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
        the rational function field F₁₆(x) [i]
      - Niederreiter sequence [i]
2. digital (96, 128, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 32, 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]

(128, 128+32, 5316)-Net over F₄ — Digital

Digital (128, 160, 5316)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+32, 2376922)-Net in Base 4 — Upper bound on s

There is no (128, 160, 2376923)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 135992 913974 574394 923383 695205 066216 513566 117483 136152 462754 351113 087961 650351 212040 481158 209635 > 4¹⁶⁰ [i]