MinT - Best Known (119−53, 119, s)-Nets in Base 4

Best Known (119−53, 119, s)-Nets in Base 4

(119−53, 119, 130)-Net over F₄ — Constructive and digital

Digital (66, 119, 130)-net over F₄, using

1 times m-reduction [i] based on digital (66, 120, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 60, 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]

(119−53, 119, 133)-Net over F₄ — Digital

Digital (66, 119, 133)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−53, 119, 1878)-Net in Base 4 — Upper bound on s

There is no (66, 119, 1879)-net in base 4, because

1 times m-reduction [i] would yield (66, 118, 1879)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 111578 646857 841095 742319 704172 034580 197284 966841 474585 007256 979260 937512 > 4¹¹⁸ [i]