MinT - Best Known (156−63, 156, s)-Nets in Base 4

Best Known (156−63, 156, s)-Nets in Base 4

(156−63, 156, 130)-Net over F₄ — Constructive and digital

Digital (93, 156, 130)-net over F₄, using

18 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 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]

(156−63, 156, 229)-Net over F₄ — Digital

Digital (93, 156, 229)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−63, 156, 4213)-Net in Base 4 — Upper bound on s

There is no (93, 156, 4214)-net in base 4, because

1 times m-reduction [i] would yield (93, 155, 4214)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2097 864673 934315 872636 897135 577455 116141 808051 245153 143007 684098 520706 565093 723518 806596 536720 > 4¹⁵⁵ [i]