MinT - Best Known (84, 159, s)-Nets in Base 4

Best Known (84, 159, s)-Nets in Base 4

(84, 159, 104)-Net over F₄ — Constructive and digital

Digital (84, 159, 104)-net over F₄, using

t-expansion [i] based on digital (73, 159, 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]

(84, 159, 141)-Net over F₄ — Digital

Digital (84, 159, 141)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 159, 1788)-Net in Base 4 — Upper bound on s

There is no (84, 159, 1789)-net in base 4, because

1 times m-reduction [i] would yield (84, 158, 1789)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 134835 711803 000052 075001 324050 880047 165965 589734 335349 972014 305984 609738 378796 968611 774633 894740 > 4¹⁵⁸ [i]