MinT - Best Known (87, 87+85, s)-Nets in Base 4

Best Known (87, 87+85, s)-Nets in Base 4

(87, 87+85, 104)-Net over F₄ — Constructive and digital

Digital (87, 172, 104)-net over F₄, using

t-expansion [i] based on digital (73, 172, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(87, 87+85, 131)-Net over F₄ — Digital

Digital (87, 172, 131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+85, 1521)-Net in Base 4 — Upper bound on s

There is no (87, 172, 1522)-net in base 4, because

1 times m-reduction [i] would yield (87, 171, 1522)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 084121 356345 966145 315725 432697 222690 039938 181600 784024 360742 193773 505875 044140 340082 847103 267562 928840 > 4¹⁷¹ [i]