MinT - Best Known (131−39, 131, s)-Nets in Base 4

Best Known (131−39, 131, s)-Nets in Base 4

(131−39, 131, 312)-Net over F₄ — Constructive and digital

Digital (92, 131, 312)-net over F₄, using

t-expansion [i] based on digital (91, 131, 312)-net over F₄, using
- 1 times m-reduction [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]

(131−39, 131, 611)-Net over F₄ — Digital

Digital (92, 131, 611)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−39, 131, 34774)-Net in Base 4 — Upper bound on s

There is no (92, 131, 34775)-net in base 4, because

1 times m-reduction [i] would yield (92, 130, 34775)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 853197 924010 849318 696613 680054 371318 891566 627941 893255 227156 139081 950880 793296 > 4¹³⁰ [i]