MinT - Best Known (133−41, 133, s)-Nets in Base 4

Best Known (133−41, 133, s)-Nets in Base 4

(133−41, 133, 312)-Net over F₄ — Constructive and digital

Digital (92, 133, 312)-net over F₄, using

4¹ times duplication [i] based on digital (91, 132, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 44, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(133−41, 133, 533)-Net over F₄ — Digital

Digital (92, 133, 533)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−41, 133, 26032)-Net in Base 4 — Upper bound on s

There is no (92, 133, 26033)-net in base 4, because

1 times m-reduction [i] would yield (92, 132, 26033)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 660322 776873 166116 231698 218976 348063 897005 397085 066155 456436 137331 412499 639624 > 4¹³² [i]