MinT - Best Known (150, 150+75, s)-Nets in Base 4

Best Known (150, 150+75, s)-Nets in Base 4

(150, 150+75, 195)-Net over F₄ — Constructive and digital

Digital (150, 225, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 75, 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]

(150, 150+75, 240)-Net in Base 4 — Constructive

(150, 225, 240)-net in base 4, using

t-expansion [i] based on (149, 225, 240)-net in base 4, using
- 5 times m-reduction [i] based on (149, 230, 240)-net in base 4, using
  - trace code for nets [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]

(150, 150+75, 610)-Net over F₄ — Digital

Digital (150, 225, 610)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+75, 21531)-Net in Base 4 — Upper bound on s

There is no (150, 225, 21532)-net in base 4, because

1 times m-reduction [i] would yield (150, 224, 21532)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 726 909450 813966 530414 224683 923291 229593 279038 277626 153188 368648 935385 159846 754063 217839 095337 503611 782941 374352 788121 639282 496167 930560 > 4²²⁴ [i]