MinT - Best Known (176−57, 176, s)-Nets in Base 4

Best Known (176−57, 176, s)-Nets in Base 4

(176−57, 176, 240)-Net over F₄ — Constructive and digital

Digital (119, 176, 240)-net over F₄, using

1 times m-reduction [i] based on digital (119, 177, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 59, 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]

(176−57, 176, 549)-Net over F₄ — Digital

Digital (119, 176, 549)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−57, 176, 21792)-Net in Base 4 — Upper bound on s

There is no (119, 176, 21793)-net in base 4, because

1 times m-reduction [i] would yield (119, 175, 21793)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2295 407436 739849 929280 605565 172777 366933 040885 677833 887772 552358 223806 487848 650930 632769 600326 333119 224120 > 4¹⁷⁵ [i]