MinT - Best Known (185−46, 185, s)-Nets in Base 4

Best Known (185−46, 185, s)-Nets in Base 4

(185−46, 185, 1028)-Net over F₄ — Constructive and digital

Digital (139, 185, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (138, 184, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 46, 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]

(185−46, 185, 1777)-Net over F₄ — Digital

Digital (139, 185, 1777)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−46, 185, 218753)-Net in Base 4 — Upper bound on s

There is no (139, 185, 218754)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2405 109172 129632 908491 186048 527138 666499 301413 599716 243859 296456 110687 160832 208988 143973 763783 859114 090421 488192 > 4¹⁸⁵ [i]