MinT - Best Known (182−83, 182, s)-Nets in Base 4

Best Known (182−83, 182, s)-Nets in Base 4

(182−83, 182, 130)-Net over F₄ — Constructive and digital

Digital (99, 182, 130)-net over F₄, using

4 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(182−83, 182, 177)-Net over F₄ — Digital

Digital (99, 182, 177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−83, 182, 2413)-Net in Base 4 — Upper bound on s

There is no (99, 182, 2414)-net in base 4, because

1 times m-reduction [i] would yield (99, 181, 2414)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 442866 398488 010959 415382 084724 586872 284267 550587 171151 305439 997735 625842 214177 997213 825997 790091 180017 105355 > 4¹⁸¹ [i]