MinT - Best Known (197−137, 197, s)-Nets in Base 4

Best Known (197−137, 197, s)-Nets in Base 4

(197−137, 197, 66)-Net over F₄ — Constructive and digital

Digital (60, 197, 66)-net over F₄, using

t-expansion [i] based on digital (49, 197, 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]

(197−137, 197, 91)-Net over F₄ — Digital

Digital (60, 197, 91)-net over F₄, using

t-expansion [i] based on digital (50, 197, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(197−137, 197, 420)-Net in Base 4 — Upper bound on s

There is no (60, 197, 421)-net in base 4, because

1 times m-reduction [i] would yield (60, 196, 421)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11247 506814 638554 385962 381830 543153 885566 253722 059377 844892 540412 156181 219936 741911 820366 982111 173839 755329 014802 606390 > 4¹⁹⁶ [i]