MinT - Best Known (136−44, 136, s)-Nets in Base 4

Best Known (136−44, 136, s)-Nets in Base 4

(136−44, 136, 240)-Net over F₄ — Constructive and digital

Digital (92, 136, 240)-net over F₄, using

4¹ times duplication [i] based on digital (91, 135, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 45, 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]

(136−44, 136, 446)-Net over F₄ — Digital

Digital (92, 136, 446)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−44, 136, 15888)-Net in Base 4 — Upper bound on s

There is no (92, 136, 15889)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7598 685199 461135 498163 808442 247747 646902 473489 704403 665509 399305 621495 963476 320000 > 4¹³⁶ [i]