MinT - Best Known (257−55, 257, s)-Nets in Base 4

Best Known (257−55, 257, s)-Nets in Base 4

(257−55, 257, 1539)-Net over F₄ — Constructive and digital

Digital (202, 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]

(257−55, 257, 5153)-Net over F₄ — Digital

Digital (202, 257, 5153)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−55, 257, 1860805)-Net in Base 4 — Upper bound on s

There is no (202, 257, 1860806)-net in base 4, because

1 times m-reduction [i] would yield (202, 256, 1860806)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13407 856638 689772 085962 892338 549737 653616 522755 314530 367942 712127 208432 332888 820353 919111 339082 981559 229882 125590 210504 348286 584630 820974 872749 593014 079120 > 4²⁵⁶ [i]