MinT - Best Known (141, 210, s)-Nets in Base 4

Best Known (141, 210, s)-Nets in Base 4

(141, 210, 240)-Net over F₄ — Constructive and digital

Digital (141, 210, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 70, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(141, 210, 605)-Net over F₄ — Digital

Digital (141, 210, 605)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 210, 22631)-Net in Base 4 — Upper bound on s

There is no (141, 210, 22632)-net in base 4, because

1 times m-reduction [i] would yield (141, 209, 22632)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 677138 784979 006441 074757 349548 950972 049121 052976 396100 321045 199613 934652 919264 255699 027514 172847 742974 294889 835178 742692 334947 > 4²⁰⁹ [i]