MinT - Best Known (81, 156, s)-Nets in Base 4

Best Known (81, 156, s)-Nets in Base 4

(81, 156, 104)-Net over F₄ — Constructive and digital

Digital (81, 156, 104)-net over F₄, using

t-expansion [i] based on digital (73, 156, 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]

(81, 156, 131)-Net over F₄ — Digital

Digital (81, 156, 131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 156, 1595)-Net in Base 4 — Upper bound on s

There is no (81, 156, 1596)-net in base 4, because

1 times m-reduction [i] would yield (81, 155, 1596)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2125 100771 751838 020091 604035 672981 186888 895238 270280 732802 791198 855567 549249 799705 970789 390418 > 4¹⁵⁵ [i]