MinT - Best Known (52, 52+47, s)-Nets in Base 4

Best Known (52, 52+47, s)-Nets in Base 4

(52, 52+47, 66)-Net over F₄ — Constructive and digital

Digital (52, 99, 66)-net over F₄, using

t-expansion [i] based on digital (49, 99, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(52, 52+47, 94)-Net over F₄ — Digital

Digital (52, 99, 94)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+47, 1136)-Net in Base 4 — Upper bound on s

There is no (52, 99, 1137)-net in base 4, because

1 times m-reduction [i] would yield (52, 98, 1137)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 101262 029850 765795 285146 192767 754712 494296 801572 244832 547808 > 4⁹⁸ [i]