MinT - Best Known (184−46, 184, s)-Nets in Base 4

Best Known (184−46, 184, s)-Nets in Base 4

(184−46, 184, 1028)-Net over F₄ — Constructive and digital

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]

(184−46, 184, 1724)-Net over F₄ — Digital

Digital (138, 184, 1724)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−46, 184, 205956)-Net in Base 4 — Upper bound on s

There is no (138, 184, 205957)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 257481 846163 631250 878680 276134 142615 451759 960769 036406 903330 306911 594665 164631 922817 030654 131639 716611 769472 > 4¹⁸⁴ [i]