MinT - Best Known (84−39, 84, s)-Nets in Base 4

Best Known (84−39, 84, s)-Nets in Base 4

(84−39, 84, 76)-Net over F₄ — Constructive and digital

Digital (45, 84, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 42, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(84−39, 84, 88)-Net over F₄ — Digital

Digital (45, 84, 88)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−39, 84, 1112)-Net in Base 4 — Upper bound on s

There is no (45, 84, 1113)-net in base 4, because

1 times m-reduction [i] would yield (45, 83, 1113)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 94 609419 449267 675683 164778 260162 554839 855063 508200 > 4⁸³ [i]