MinT - Best Known (87, 130, s)-Nets in Base 4

Best Known (87, 130, s)-Nets in Base 4

(87, 130, 195)-Net over F₄ — Constructive and digital

Digital (87, 130, 195)-net over F₄, using

4¹ times duplication [i] based on digital (86, 129, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 43, 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]

(87, 130, 208)-Net in Base 4 — Constructive

(87, 130, 208)-net in base 4, using

trace code for nets [i] based on (22, 65, 104)-net in base 16, using
- base change [i] based on digital (9, 52, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(87, 130, 395)-Net over F₄ — Digital

Digital (87, 130, 395)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 130, 14428)-Net in Base 4 — Upper bound on s

There is no (87, 130, 14429)-net in base 4, because

1 times m-reduction [i] would yield (87, 129, 14429)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 463337 425644 644440 092063 772450 243521 851450 853317 075967 958675 268343 568485 233788 > 4¹²⁹ [i]