MinT - Best Known (175, 233, s)-Nets in Base 4

Best Known (175, 233, s)-Nets in Base 4

(175, 233, 1028)-Net over F₄ — Constructive and digital

Digital (175, 233, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (174, 232, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 58, 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]

(175, 233, 2156)-Net over F₄ — Digital

Digital (175, 233, 2156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 233, 267425)-Net in Base 4 — Upper bound on s

There is no (175, 233, 267426)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 544885 580554 594318 487687 975687 684828 753217 217666 964537 598765 300344 844101 470125 254265 536248 934619 534374 890983 068442 280813 433756 541806 014920 > 4²³³ [i]