MinT - Best Known (88, 88+67, s)-Nets in Base 4

Best Known (88, 88+67, s)-Nets in Base 4

(88, 88+67, 130)-Net over F₄ — Constructive and digital

Digital (88, 155, 130)-net over F₄, using

9 times m-reduction [i] based on digital (88, 164, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 82, 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]

(88, 88+67, 183)-Net over F₄ — Digital

Digital (88, 155, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+67, 2803)-Net in Base 4 — Upper bound on s

There is no (88, 155, 2804)-net in base 4, because

1 times m-reduction [i] would yield (88, 154, 2804)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 524 605951 492217 011135 377685 062191 129058 637449 810218 027171 974384 265932 428662 368756 973847 331705 > 4¹⁵⁴ [i]