MinT - Best Known (142, 142+65, s)-Nets in Base 4

Best Known (142, 142+65, s)-Nets in Base 4

(142, 142+65, 312)-Net over F₄ — Constructive and digital

Digital (142, 207, 312)-net over F₄, using

t-expansion [i] based on digital (141, 207, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 69, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(142, 142+65, 711)-Net over F₄ — Digital

Digital (142, 207, 711)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+65, 32001)-Net in Base 4 — Upper bound on s

There is no (142, 207, 32002)-net in base 4, because

1 times m-reduction [i] would yield (142, 206, 32002)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10585 987946 311066 494572 765276 973215 577165 515046 910685 153228 867761 251683 233193 540993 385280 830838 102062 844302 751523 173981 461400 > 4²⁰⁶ [i]