MinT - Best Known (146, 219, s)-Nets in Base 4

Best Known (146, 219, s)-Nets in Base 4

(146, 219, 195)-Net over F₄ — Constructive and digital

Digital (146, 219, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 73, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(146, 219, 240)-Net in Base 4 — Constructive

(146, 219, 240)-net in base 4, using

5 times m-reduction [i] based on (146, 224, 240)-net in base 4, using
- trace code for nets [i] based on (34, 112, 120)-net in base 16, using
  - 3 times m-reduction [i] based on (34, 115, 120)-net in base 16, using
    - base change [i] based on digital (11, 92, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(146, 219, 595)-Net over F₄ — Digital

Digital (146, 219, 595)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 219, 21028)-Net in Base 4 — Upper bound on s

There is no (146, 219, 21029)-net in base 4, because

1 times m-reduction [i] would yield (146, 218, 21029)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177503 061071 947312 027590 208985 931420 262401 892846 083707 442447 105477 168084 054161 985176 504942 007992 855551 168707 349794 606235 293248 640001 > 4²¹⁸ [i]