MinT - Best Known (252−49, 252, s)-Nets in Base 4

Best Known (252−49, 252, s)-Nets in Base 4

(252−49, 252, 1539)-Net over F₄ — Constructive and digital

Digital (203, 252, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 252, 1539)-net over F₄, using
- 6 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]

(252−49, 252, 9070)-Net over F₄ — Digital

Digital (203, 252, 9070)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−49, 252, 6468212)-Net in Base 4 — Upper bound on s

There is no (203, 252, 6468213)-net in base 4, because

1 times m-reduction [i] would yield (203, 251, 6468213)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 093609 231458 913816 259450 171418 091342 274243 322771 286425 120395 449656 107376 577327 837493 385443 600821 728197 509255 739328 633776 801165 128119 390480 837885 049756 > 4²⁵¹ [i]