MinT - Best Known (110, 110+51, s)-Nets in Base 4

Best Known (110, 110+51, s)-Nets in Base 4

(110, 110+51, 240)-Net over F₄ — Constructive and digital

Digital (110, 161, 240)-net over F₄, using

t-expansion [i] based on digital (109, 161, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (109, 162, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 54, 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]

(110, 110+51, 556)-Net over F₄ — Digital

Digital (110, 161, 556)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+51, 24172)-Net in Base 4 — Upper bound on s

There is no (110, 161, 24173)-net in base 4, because

1 times m-reduction [i] would yield (110, 160, 24173)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 136857 018131 880406 664640 620307 782958 110400 824487 338729 639483 926531 142443 586722 075204 023839 695232 > 4¹⁶⁰ [i]