MinT - Best Known (127, 127+61, s)-Nets in Base 4

Best Known (127, 127+61, s)-Nets in Base 4

(127, 127+61, 240)-Net over F₄ — Constructive and digital

Digital (127, 188, 240)-net over F₄, using

1 times m-reduction [i] based on digital (127, 189, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 63, 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]

(127, 127+61, 577)-Net over F₄ — Digital

Digital (127, 188, 577)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+61, 22700)-Net in Base 4 — Upper bound on s

There is no (127, 188, 22701)-net in base 4, because

1 times m-reduction [i] would yield (127, 187, 22701)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38492 415434 648326 314960 568761 828628 105001 600878 234447 233464 200916 733662 996739 231191 903841 492211 512502 917721 512112 > 4¹⁸⁷ [i]