MinT - Best Known (244−143, 244, s)-Nets in Base 4

Best Known (244−143, 244, s)-Nets in Base 4

(244−143, 244, 104)-Net over F₄ — Constructive and digital

Digital (101, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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]

(244−143, 244, 144)-Net over F₄ — Digital

Digital (101, 244, 144)-net over F₄, using

t-expansion [i] based on digital (91, 244, 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]

(244−143, 244, 987)-Net in Base 4 — Upper bound on s

There is no (101, 244, 988)-net in base 4, because

1 times m-reduction [i] would yield (101, 243, 988)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 207 187276 526454 349772 137936 167805 901873 196649 349824 844882 978994 286210 403340 813886 966248 484499 154586 211974 088040 920941 159501 819475 317541 259991 183390 > 4²⁴³ [i]