MinT - Best Known (138−44, 138, s)-Nets in Base 4

Best Known (138−44, 138, s)-Nets in Base 4

(138−44, 138, 240)-Net over F₄ — Constructive and digital

Digital (94, 138, 240)-net over F₄, using

t-expansion [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]

(138−44, 138, 478)-Net over F₄ — Digital

Digital (94, 138, 478)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−44, 138, 18024)-Net in Base 4 — Upper bound on s

There is no (94, 138, 18025)-net in base 4, because

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]