MinT - Best Known (59, 59+39, s)-Nets in Base 4

Best Known (59, 59+39, s)-Nets in Base 4

(59, 59+39, 130)-Net over F₄ — Constructive and digital

Digital (59, 98, 130)-net over F₄, using

8 times m-reduction [i] based on digital (59, 106, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 53, 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]

(59, 59+39, 165)-Net over F₄ — Digital

Digital (59, 98, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+39, 3116)-Net in Base 4 — Upper bound on s

There is no (59, 98, 3117)-net in base 4, because

1 times m-reduction [i] would yield (59, 97, 3117)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25212 989781 134405 612026 733569 344239 835835 709466 761117 662168 > 4⁹⁷ [i]