MinT - Best Known (153−49, 153, s)-Nets in Base 4

Best Known (153−49, 153, s)-Nets in Base 4

(153−49, 153, 240)-Net over F₄ — Constructive and digital

Digital (104, 153, 240)-net over F₄, using

t-expansion [i] based on digital (103, 153, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 51, 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]

(153−49, 153, 510)-Net over F₄ — Digital

Digital (104, 153, 510)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−49, 153, 21227)-Net in Base 4 — Upper bound on s

There is no (104, 153, 21228)-net in base 4, because

1 times m-reduction [i] would yield (104, 152, 21228)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 627903 517047 464512 531424 850526 609571 218211 585838 681005 732051 843027 127682 639176 254083 088486 > 4¹⁵² [i]