MinT - Best Known (142−45, 142, s)-Nets in Base 4

Best Known (142−45, 142, s)-Nets in Base 4

(142−45, 142, 240)-Net over F₄ — Constructive and digital

Digital (97, 142, 240)-net over F₄, using

2 times m-reduction [i] based on digital (97, 144, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 48, 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]

(142−45, 142, 501)-Net over F₄ — Digital

Digital (97, 142, 501)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−45, 142, 21778)-Net in Base 4 — Upper bound on s

There is no (97, 142, 21779)-net in base 4, because

1 times m-reduction [i] would yield (97, 141, 21779)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 772369 136882 593698 639105 750158 613870 749831 401263 184068 481520 058023 764851 419371 026240 > 4¹⁴¹ [i]