MinT - Best Known (118−37, 118, s)-Nets in Base 4

Best Known (118−37, 118, s)-Nets in Base 4

(118−37, 118, 240)-Net over F₄ — Constructive and digital

Digital (81, 118, 240)-net over F₄, using

2 times m-reduction [i] based on digital (81, 120, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 40, 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]

(118−37, 118, 453)-Net over F₄ — Digital

Digital (81, 118, 453)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−37, 118, 20610)-Net in Base 4 — Upper bound on s

There is no (81, 118, 20611)-net in base 4, because

1 times m-reduction [i] would yield (81, 117, 20611)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27613 458646 153044 124948 691265 578933 869425 577788 013155 761417 695681 602040 > 4¹¹⁷ [i]