MinT - Best Known (186−87, 186, s)-Nets in Base 4

Best Known (186−87, 186, s)-Nets in Base 4

(186−87, 186, 130)-Net over F₄ — Constructive and digital

Digital (99, 186, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 93, 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]

(186−87, 186, 166)-Net over F₄ — Digital

Digital (99, 186, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−87, 186, 2155)-Net in Base 4 — Upper bound on s

There is no (99, 186, 2156)-net in base 4, because

1 times m-reduction [i] would yield (99, 185, 2156)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2419 278661 034689 233334 575697 387131 214347 616704 132037 636210 802746 264689 850828 829833 487840 944123 914770 959729 218169 > 4¹⁸⁵ [i]