MinT - Best Known (258−51, 258, s)-Nets in Base 4

Best Known (258−51, 258, s)-Nets in Base 4

(258−51, 258, 1539)-Net over F₄ — Constructive and digital

Digital (207, 258, 1539)-net over F₄, using

t-expansion [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]

(258−51, 258, 8326)-Net over F₄ — Digital

Digital (207, 258, 8326)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−51, 258, 5244204)-Net in Base 4 — Upper bound on s

There is no (207, 258, 5244205)-net in base 4, because

1 times m-reduction [i] would yield (207, 257, 5244205)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53631 419585 441027 355839 179771 065998 519253 572237 396993 725384 300329 819036 683845 621036 860217 508018 424907 599067 845058 379562 063871 866481 635518 056468 923273 077248 > 4²⁵⁷ [i]