MinT - Best Known (146−47, 146, s)-Nets in Base 4

Best Known (146−47, 146, s)-Nets in Base 4

(146−47, 146, 240)-Net over F₄ — Constructive and digital

Digital (99, 146, 240)-net over F₄, using

1 times m-reduction [i] based on digital (99, 147, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 49, 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]

(146−47, 146, 481)-Net over F₄ — Digital

Digital (99, 146, 481)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−47, 146, 19611)-Net in Base 4 — Upper bound on s

There is no (99, 146, 19612)-net in base 4, because

1 times m-reduction [i] would yield (99, 145, 19612)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1989 743373 175852 956581 128470 212226 546660 785330 476440 481494 443859 120183 964958 414542 410658 > 4¹⁴⁵ [i]