MinT - Best Known (197−121, 197, s)-Nets in Base 4

Best Known (197−121, 197, s)-Nets in Base 4

(197−121, 197, 104)-Net over F₄ — Constructive and digital

Digital (76, 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]

(197−121, 197, 112)-Net over F₄ — Digital

Digital (76, 197, 112)-net over F₄, using

t-expansion [i] based on digital (73, 197, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(197−121, 197, 667)-Net in Base 4 — Upper bound on s

There is no (76, 197, 668)-net in base 4, because

1 times m-reduction [i] would yield (76, 196, 668)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10246 268293 774829 386631 575517 639523 721276 760264 110737 711827 779954 102272 097033 901057 816413 150243 408667 449750 255480 705120 > 4¹⁹⁶ [i]