MinT - Best Known (159−63, 159, s)-Nets in Base 4

Best Known (159−63, 159, s)-Nets in Base 4

(159−63, 159, 130)-Net over F₄ — Constructive and digital

Digital (96, 159, 130)-net over F₄, using

21 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(159−63, 159, 248)-Net over F₄ — Digital

Digital (96, 159, 248)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−63, 159, 4821)-Net in Base 4 — Upper bound on s

There is no (96, 159, 4822)-net in base 4, because

1 times m-reduction [i] would yield (96, 158, 4822)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133716 695329 444768 310689 824348 711219 643982 582296 199804 914574 100656 606573 701359 118818 466879 992160 > 4¹⁵⁸ [i]