MinT - Best Known (71, 71+45, s)-Nets in Base 4

Best Known (71, 71+45, s)-Nets in Base 4

(71, 71+45, 130)-Net over F₄ — Constructive and digital

Digital (71, 116, 130)-net over F₄, using

14 times m-reduction [i] based on digital (71, 130, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 65, 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]

(71, 71+45, 205)-Net over F₄ — Digital

Digital (71, 116, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+45, 4217)-Net in Base 4 — Upper bound on s

There is no (71, 116, 4218)-net in base 4, because

1 times m-reduction [i] would yield (71, 115, 4218)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1731 772209 234847 594703 474362 891438 449814 061873 923252 944434 985057 035572 > 4¹¹⁵ [i]