MinT - Best Known (89−25, 89, s)-Nets in Base 4

Best Known (89−25, 89, s)-Nets in Base 4

(89−25, 89, 312)-Net over F₄ — Constructive and digital

Digital (64, 89, 312)-net over F₄, using

t-expansion [i] based on digital (63, 89, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (63, 90, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 30, 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]

(89−25, 89, 570)-Net over F₄ — Digital

Digital (64, 89, 570)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−25, 89, 45841)-Net in Base 4 — Upper bound on s

There is no (64, 89, 45842)-net in base 4, because

1 times m-reduction [i] would yield (64, 88, 45842)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 95798 912635 044106 431882 621121 114804 047209 052425 442220 > 4⁸⁸ [i]