MinT - Best Known (82, 121, s)-Nets in Base 4

Best Known (82, 121, s)-Nets in Base 4

(82, 121, 240)-Net over F₄ — Constructive and digital

Digital (82, 121, 240)-net over F₄, using

4¹ times duplication [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]

(82, 121, 413)-Net over F₄ — Digital

Digital (82, 121, 413)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 121, 16756)-Net in Base 4 — Upper bound on s

There is no (82, 121, 16757)-net in base 4, because

1 times m-reduction [i] would yield (82, 120, 16757)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 768002 053757 469311 924842 431462 025801 293580 050879 133859 247578 116280 139852 > 4¹²⁰ [i]