MinT - Best Known (232−49, 232, s)-Nets in Base 4

Best Known (232−49, 232, s)-Nets in Base 4

(232−49, 232, 1539)-Net over F₄ — Constructive and digital

Digital (183, 232, 1539)-net over F₄, using

4¹ times duplication [i] based on digital (182, 231, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 77, 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]

(232−49, 232, 5101)-Net over F₄ — Digital

Digital (183, 232, 5101)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−49, 232, 2037345)-Net in Base 4 — Upper bound on s

There is no (183, 232, 2037346)-net in base 4, because

1 times m-reduction [i] would yield (183, 231, 2037346)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 908558 311357 993881 436141 666443 877525 256399 593824 322357 673567 466867 679111 184100 444673 658927 757184 466189 197666 501391 989427 191375 970137 102436 > 4²³¹ [i]