MinT - Best Known (167−63, 167, s)-Nets in Base 4

Best Known (167−63, 167, s)-Nets in Base 4

(167−63, 167, 130)-Net over F₄ — Constructive and digital

Digital (104, 167, 130)-net over F₄, using

29 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(167−63, 167, 305)-Net over F₄ — Digital

Digital (104, 167, 305)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−63, 167, 6906)-Net in Base 4 — Upper bound on s

There is no (104, 167, 6907)-net in base 4, because

1 times m-reduction [i] would yield (104, 166, 6907)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8768 609062 908483 241930 850081 864524 733257 301575 301120 915993 117179 792922 554047 544550 527643 747105 660608 > 4¹⁶⁶ [i]