MinT - Best Known (199, 199+51, s)-Nets in Base 4

Best Known (199, 199+51, s)-Nets in Base 4

(199, 199+51, 1539)-Net over F₄ — Constructive and digital

Digital (199, 250, 1539)-net over F₄, using

t-expansion [i] based on digital (198, 250, 1539)-net over F₄, using
- 5 times m-reduction [i] based on digital (198, 255, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 85, 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]

(199, 199+51, 6675)-Net over F₄ — Digital

Digital (199, 250, 6675)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199, 199+51, 3365266)-Net in Base 4 — Upper bound on s

There is no (199, 250, 3365267)-net in base 4, because

1 times m-reduction [i] would yield (199, 249, 3365267)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818350 704469 617921 197644 359263 446869 599063 155540 886053 524319 893433 413986 705380 626322 681839 652824 795217 267223 788150 875856 472337 258025 672297 176486 310624 > 4²⁴⁹ [i]