MinT - Best Known (169−71, 169, s)-Nets in Base 4

Best Known (169−71, 169, s)-Nets in Base 4

(169−71, 169, 130)-Net over F₄ — Constructive and digital

Digital (98, 169, 130)-net over F₄, using

15 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(169−71, 169, 215)-Net over F₄ — Digital

Digital (98, 169, 215)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−71, 169, 3569)-Net in Base 4 — Upper bound on s

There is no (98, 169, 3570)-net in base 4, because

1 times m-reduction [i] would yield (98, 168, 3570)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 141123 492666 739345 635810 137439 109831 162172 987202 499776 600501 257952 300910 020769 097447 607441 002585 523880 > 4¹⁶⁸ [i]