MinT - Best Known (108, 108+51, s)-Nets in Base 4

Best Known (108, 108+51, s)-Nets in Base 4

(108, 108+51, 240)-Net over F₄ — Constructive and digital

Digital (108, 159, 240)-net over F₄, using

t-expansion [i] based on digital (107, 159, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 53, 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]

(108, 108+51, 524)-Net over F₄ — Digital

Digital (108, 159, 524)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+51, 21632)-Net in Base 4 — Upper bound on s

There is no (108, 159, 21633)-net in base 4, because

1 times m-reduction [i] would yield (108, 158, 21633)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133506 078413 283149 366248 248713 000165 718344 076727 473325 755804 346802 529769 876471 876400 780674 081984 > 4¹⁵⁸ [i]