MinT - Best Known (97, 97+67, s)-Nets in Base 4

Best Known (97, 97+67, s)-Nets in Base 4

(97, 97+67, 130)-Net over F₄ — Constructive and digital

Digital (97, 164, 130)-net over F₄, using

18 times m-reduction [i] based on digital (97, 182, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 91, 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]

(97, 97+67, 230)-Net over F₄ — Digital

Digital (97, 164, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+67, 4103)-Net in Base 4 — Upper bound on s

There is no (97, 164, 4104)-net in base 4, because

1 times m-reduction [i] would yield (97, 163, 4104)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 136 742278 885178 579396 239397 970502 474936 511107 365504 697317 104726 013533 907701 515406 148652 988956 348288 > 4¹⁶³ [i]