MinT - Best Known (197−93, 197, s)-Nets in Base 4

Best Known (197−93, 197, s)-Nets in Base 4

(197−93, 197, 104)-Net over F₄ — Constructive and digital

Digital (104, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(197−93, 197, 170)-Net over F₄ — Digital

Digital (104, 197, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−93, 197, 2167)-Net in Base 4 — Upper bound on s

There is no (104, 197, 2168)-net in base 4, because

1 times m-reduction [i] would yield (104, 196, 2168)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10212 257115 414645 905615 852642 586257 861738 197251 069113 090261 001937 461888 475184 838542 691531 487754 980808 452216 692044 740870 > 4¹⁹⁶ [i]