MinT - Best Known (88, 88+39, s)-Nets in Base 4

Best Known (88, 88+39, s)-Nets in Base 4

(88, 88+39, 312)-Net over F₄ — Constructive and digital

Digital (88, 127, 312)-net over F₄, using

4¹ times duplication [i] based on digital (87, 126, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 42, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(88, 88+39, 523)-Net over F₄ — Digital

Digital (88, 127, 523)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+39, 25968)-Net in Base 4 — Upper bound on s

There is no (88, 127, 25969)-net in base 4, because

1 times m-reduction [i] would yield (88, 126, 25969)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7239 825597 618072 692352 270486 663116 690607 085619 415123 172035 872999 329446 200608 > 4¹²⁶ [i]