MinT - Best Known (102, 102+143, s)-Nets in Base 4

Best Known (102, 102+143, s)-Nets in Base 4

(102, 102+143, 104)-Net over F₄ — Constructive and digital

Digital (102, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 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]

(102, 102+143, 144)-Net over F₄ — Digital

Digital (102, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(102, 102+143, 1008)-Net in Base 4 — Upper bound on s

There is no (102, 245, 1009)-net in base 4, because

1 times m-reduction [i] would yield (102, 244, 1009)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 851 696666 361639 031953 644696 272381 574669 369146 801775 899058 837901 936515 309800 611664 582454 308497 925648 334998 255544 007217 775425 531694 345440 388997 905872 > 4²⁴⁴ [i]