MinT - Best Known (147−57, 147, s)-Nets in Base 4

Best Known (147−57, 147, s)-Nets in Base 4

(147−57, 147, 130)-Net over F₄ — Constructive and digital

Digital (90, 147, 130)-net over F₄, using

21 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(147−57, 147, 250)-Net over F₄ — Digital

Digital (90, 147, 250)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−57, 147, 5167)-Net in Base 4 — Upper bound on s

There is no (90, 147, 5168)-net in base 4, because

1 times m-reduction [i] would yield (90, 146, 5168)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7976 316004 206935 066847 878467 713388 427986 618871 252788 496666 424327 081187 641206 533533 213670 > 4¹⁴⁶ [i]