MinT - Best Known (103, 103+81, s)-Nets in Base 4

Best Known (103, 103+81, s)-Nets in Base 4

(103, 103+81, 130)-Net over F₄ — Constructive and digital

Digital (103, 184, 130)-net over F₄, using

10 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(103, 103+81, 200)-Net over F₄ — Digital

Digital (103, 184, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+81, 2953)-Net in Base 4 — Upper bound on s

There is no (103, 184, 2954)-net in base 4, because

1 times m-reduction [i] would yield (103, 183, 2954)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 151 650756 846156 308680 626189 552873 466603 783039 088674 946894 348181 391912 214635 403803 408042 331634 134292 207640 162612 > 4¹⁸³ [i]