MinT - Best Known (83−27, 83, s)-Nets in Base 4

Best Known (83−27, 83, s)-Nets in Base 4

(83−27, 83, 195)-Net over F₄ — Constructive and digital

Digital (56, 83, 195)-net over F₄, using

1 times m-reduction [i] based on digital (56, 84, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 28, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(83−27, 83, 303)-Net over F₄ — Digital

Digital (56, 83, 303)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−27, 83, 11844)-Net in Base 4 — Upper bound on s

There is no (56, 83, 11845)-net in base 4, because

1 times m-reduction [i] would yield (56, 82, 11845)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 397708 420552 644254 979239 322755 617531 080516 151520 > 4⁸² [i]