MinT - Best Known (102, 102+78, s)-Nets in Base 4

Best Known (102, 102+78, s)-Nets in Base 4

(102, 102+78, 130)-Net over F₄ — Constructive and digital

Digital (102, 180, 130)-net over F₄, using

12 times m-reduction [i] based on digital (102, 192, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 96, 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]

(102, 102+78, 206)-Net over F₄ — Digital

Digital (102, 180, 206)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+78, 3051)-Net in Base 4 — Upper bound on s

There is no (102, 180, 3052)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 359982 715987 698040 977645 694028 890420 821126 256592 446797 230626 129061 276298 392740 694967 633413 621524 564761 130970 > 4¹⁸⁰ [i]