MinT - Best Known (87−25, 87, s)-Nets in Base 4

Best Known (87−25, 87, s)-Nets in Base 4

(87−25, 87, 312)-Net over F₄ — Constructive and digital

Digital (62, 87, 312)-net over F₄, using

t-expansion [i] based on digital (61, 87, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 29, 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]

(87−25, 87, 509)-Net over F₄ — Digital

Digital (62, 87, 509)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−25, 87, 36382)-Net in Base 4 — Upper bound on s

There is no (62, 87, 36383)-net in base 4, because

1 times m-reduction [i] would yield (62, 86, 36383)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5987 708395 356881 274262 470294 349517 758476 083315 324665 > 4⁸⁶ [i]