MinT - Best Known (128−41, 128, s)-Nets in Base 4

Best Known (128−41, 128, s)-Nets in Base 4

(128−41, 128, 240)-Net over F₄ — Constructive and digital

Digital (87, 128, 240)-net over F₄, using

1 times m-reduction [i] based on digital (87, 129, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 43, 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]

(128−41, 128, 442)-Net over F₄ — Digital

Digital (87, 128, 442)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−41, 128, 18402)-Net in Base 4 — Upper bound on s

There is no (87, 128, 18403)-net in base 4, because

1 times m-reduction [i] would yield (87, 127, 18403)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28953 258237 027533 275690 949182 585993 674406 044424 263931 154426 716837 936260 044296 > 4¹²⁷ [i]