MinT - Best Known (173−73, 173, s)-Nets in Base 4

Best Known (173−73, 173, s)-Nets in Base 4

(173−73, 173, 130)-Net over F₄ — Constructive and digital

Digital (100, 173, 130)-net over F₄, using

15 times m-reduction [i] based on digital (100, 188, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 94, 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]

(173−73, 173, 217)-Net over F₄ — Digital

Digital (100, 173, 217)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−73, 173, 3552)-Net in Base 4 — Upper bound on s

There is no (100, 173, 3553)-net in base 4, because

1 times m-reduction [i] would yield (100, 172, 3553)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 985548 937618 695133 683826 749270 937721 928507 805654 746983 185880 447248 882544 997050 053847 980382 395941 988400 > 4¹⁷² [i]