MinT - Best Known (254−51, 254, s)-Nets in Base 4

Best Known (254−51, 254, s)-Nets in Base 4

(254−51, 254, 1539)-Net over F₄ — Constructive and digital

Digital (203, 254, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 254, 1539)-net over F₄, using
- 4 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]

(254−51, 254, 7455)-Net over F₄ — Digital

Digital (203, 254, 7455)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−51, 254, 4200970)-Net in Base 4 — Upper bound on s

There is no (203, 254, 4200971)-net in base 4, because

1 times m-reduction [i] would yield (203, 253, 4200971)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 498215 851217 192199 512425 865338 388806 399530 037648 293270 142584 476792 472500 221981 429161 978834 753741 834520 697052 752733 659687 402352 990484 609828 358356 267328 > 4²⁵³ [i]