MinT - Best Known (254−53, 254, s)-Nets in Base 4

Best Known (254−53, 254, s)-Nets in Base 4

(254−53, 254, 1539)-Net over F₄ — Constructive and digital

Digital (201, 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]

(254−53, 254, 5909)-Net over F₄ — Digital

Digital (201, 254, 5909)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−53, 254, 2539071)-Net in Base 4 — Upper bound on s

There is no (201, 254, 2539072)-net in base 4, because

1 times m-reduction [i] would yield (201, 253, 2539072)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 497164 585096 017879 459107 112237 870745 556018 297338 599666 555361 362885 717703 764471 353592 081428 232998 071436 480610 510402 698395 013236 224126 883102 374449 492045 > 4²⁵³ [i]