MinT - Best Known (155−51, 155, s)-Nets in Base 4

Best Known (155−51, 155, s)-Nets in Base 4

(155−51, 155, 195)-Net over F₄ — Constructive and digital

Digital (104, 155, 195)-net over F₄, using

1 times m-reduction [i] based on digital (104, 156, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 52, 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]

(155−51, 155, 208)-Net in Base 4 — Constructive

(104, 155, 208)-net in base 4, using

3 times m-reduction [i] based on (104, 158, 208)-net in base 4, using
- trace code for nets [i] based on (25, 79, 104)-net in base 16, using
  - 1 times m-reduction [i] based on (25, 80, 104)-net in base 16, using
    - base change [i] based on digital (9, 64, 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]

(155−51, 155, 465)-Net over F₄ — Digital

Digital (104, 155, 465)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−51, 155, 17325)-Net in Base 4 — Upper bound on s

There is no (104, 155, 17326)-net in base 4, because

1 times m-reduction [i] would yield (104, 154, 17326)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 881780 856105 551029 833314 543963 418202 384944 110269 413134 030748 325709 731430 767382 449113 478298 > 4¹⁵⁴ [i]