MinT - Best Known (167−72, 167, s)-Nets in Base 4

Best Known (167−72, 167, s)-Nets in Base 4

(167−72, 167, 130)-Net over F₄ — Constructive and digital

Digital (95, 167, 130)-net over F₄, using

11 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(167−72, 167, 196)-Net over F₄ — Digital

Digital (95, 167, 196)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−72, 167, 2925)-Net in Base 4 — Upper bound on s

There is no (95, 167, 2926)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35314 259659 662575 851677 719748 437732 715742 750009 683776 522250 933684 621106 342732 138455 977678 688503 409385 > 4¹⁶⁷ [i]