MinT - Best Known (132−41, 132, s)-Nets in Base 4

Best Known (132−41, 132, s)-Nets in Base 4

(132−41, 132, 312)-Net over F₄ — Constructive and digital

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]

(132−41, 132, 513)-Net over F₄ — Digital

Digital (91, 132, 513)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−41, 132, 24287)-Net in Base 4 — Upper bound on s

There is no (91, 132, 24288)-net in base 4, because

1 times m-reduction [i] would yield (91, 131, 24288)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 411629 243498 838661 561051 640912 329401 718140 441812 159718 867713 116808 859391 248231 > 4¹³¹ [i]