MinT - Best Known (150−50, 150, s)-Nets in Base 4

Best Known (150−50, 150, s)-Nets in Base 4

(150−50, 150, 195)-Net over F₄ — Constructive and digital

Digital (100, 150, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 50, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(150−50, 150, 208)-Net in Base 4 — Constructive

(100, 150, 208)-net in base 4, using

t-expansion [i] based on (99, 150, 208)-net in base 4, using
- trace code for nets [i] based on (24, 75, 104)-net in base 16, using
  - base change [i] based on digital (9, 60, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(150−50, 150, 431)-Net over F₄ — Digital

Digital (100, 150, 431)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−50, 150, 13874)-Net in Base 4 — Upper bound on s

There is no (100, 150, 13875)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 037515 743499 107305 296357 114789 078905 020650 802719 144053 597503 037144 696971 756897 744815 742616 > 4¹⁵⁰ [i]