MinT - Best Known (146, 146+48, s)-Nets in Base 4

Best Known (146, 146+48, s)-Nets in Base 4

(146, 146+48, 1028)-Net over F₄ — Constructive and digital

Digital (146, 194, 1028)-net over F₄, using

4² times duplication [i] based on digital (144, 192, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 48, 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]

(146, 146+48, 1894)-Net over F₄ — Digital

Digital (146, 194, 1894)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+48, 240357)-Net in Base 4 — Upper bound on s

There is no (146, 194, 240358)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 457701 406590 753976 461546 045275 076258 300598 622094 525686 143451 268876 347115 043378 956190 092755 895444 957962 893014 998764 > 4¹⁹⁴ [i]