MinT - Best Known (139−45, 139, s)-Nets in Base 4

Best Known (139−45, 139, s)-Nets in Base 4

(139−45, 139, 240)-Net over F₄ — Constructive and digital

Digital (94, 139, 240)-net over F₄, using

4¹ times duplication [i] based on digital (93, 138, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 46, 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]

(139−45, 139, 453)-Net over F₄ — Digital

Digital (94, 139, 453)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−45, 139, 18024)-Net in Base 4 — Upper bound on s

There is no (94, 139, 18025)-net in base 4, because

1 times m-reduction [i] would yield (94, 138, 18025)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 121507 093677 099439 570147 773034 356180 626531 745230 483074 406985 308748 478511 279554 850296 > 4¹³⁸ [i]