MinT - Best Known (257−53, 257, s)-Nets in Base 4

Best Known (257−53, 257, s)-Nets in Base 4

(257−53, 257, 1539)-Net over F₄ — Constructive and digital

Digital (204, 257, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 257, 1539)-net over F₄, using
- 1 times m-reduction [i] based on digital (200, 258, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(257−53, 257, 6399)-Net over F₄ — Digital

Digital (204, 257, 6399)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−53, 257, 2979504)-Net in Base 4 — Upper bound on s

There is no (204, 257, 2979505)-net in base 4, because

1 times m-reduction [i] would yield (204, 256, 2979505)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13407 904099 871755 673326 900080 985110 126102 680073 426077 021188 094665 827512 493467 412726 229707 377159 080254 370437 860895 473745 447114 431992 523609 639131 158134 282224 > 4²⁵⁶ [i]