MinT - Best Known (134−41, 134, s)-Nets in Base 4

Best Known (134−41, 134, s)-Nets in Base 4

(134−41, 134, 312)-Net over F₄ — Constructive and digital

Digital (93, 134, 312)-net over F₄, using

1 times m-reduction [i] based on digital (93, 135, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 45, 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]

(134−41, 134, 553)-Net over F₄ — Digital

Digital (93, 134, 553)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−41, 134, 27901)-Net in Base 4 — Upper bound on s

There is no (93, 134, 27902)-net in base 4, because

1 times m-reduction [i] would yield (93, 133, 27902)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 118 587049 376693 223100 119600 431373 766378 061705 960499 751217 449151 540719 719106 224871 > 4¹³³ [i]