MinT - Best Known (88, 132, s)-Nets in Base 4

Best Known (88, 132, s)-Nets in Base 4

(88, 132, 195)-Net over F₄ — Constructive and digital

Digital (88, 132, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 44, 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]

(88, 132, 196)-Net in Base 4 — Constructive

(88, 132, 196)-net in base 4, using

2 times m-reduction [i] based on (88, 134, 196)-net in base 4, using
- trace code for nets [i] based on (21, 67, 98)-net in base 16, using
  - 3 times m-reduction [i] based on (21, 70, 98)-net in base 16, using
    - base change [i] based on digital (7, 56, 98)-net over F₃₂, using
      - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]

(88, 132, 388)-Net over F₄ — Digital

Digital (88, 132, 388)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 132, 12344)-Net in Base 4 — Upper bound on s

There is no (88, 132, 12345)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 681760 660607 387967 012785 411711 312422 199253 907515 694384 136562 633921 522604 711004 > 4¹³² [i]