MinT - Best Known (102, 102+83, s)-Nets in Base 4

Best Known (102, 102+83, s)-Nets in Base 4

(102, 102+83, 130)-Net over F₄ — Constructive and digital

Digital (102, 185, 130)-net over F₄, using

7 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+83, 189)-Net over F₄ — Digital

Digital (102, 185, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+83, 2674)-Net in Base 4 — Upper bound on s

There is no (102, 185, 2675)-net in base 4, because

1 times m-reduction [i] would yield (102, 184, 2675)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 829050 093963 003834 439844 466763 421816 939574 910204 346032 429266 548020 879338 394518 626683 469648 824237 315471 294332 > 4¹⁸⁴ [i]