MinT - Best Known (244−137, 244, s)-Nets in Base 4

Best Known (244−137, 244, s)-Nets in Base 4

(244−137, 244, 130)-Net over F₄ — Constructive and digital

Digital (107, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(244−137, 244, 144)-Net over F₄ — Digital

Digital (107, 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]

(244−137, 244, 1180)-Net in Base 4 — Upper bound on s

There is no (107, 244, 1181)-net in base 4, because

1 times m-reduction [i] would yield (107, 243, 1181)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 205 202784 812712 048945 797898 192107 074765 475582 778258 571159 827136 324931 430561 833318 052333 713403 817081 148539 510521 971624 252513 228450 985775 616855 759866 > 4²⁴³ [i]