MinT - Best Known (48, 48+16, s)-Nets in Base 4

Best Known (48, 48+16, s)-Nets in Base 4

(48, 48+16, 1028)-Net over F₄ — Constructive and digital

Digital (48, 64, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 16, 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]

(48, 48+16, 82227)-Net in Base 4 — Upper bound on s

There is no (48, 64, 82228)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 340 304641 720299 525696 498368 117963 160010 > 4⁶⁴ [i]