MinT - Best Known (90, 244, s)-Nets in Base 4

Best Known (90, 244, s)-Nets in Base 4

(90, 244, 104)-Net over F₄ — Constructive and digital

Digital (90, 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]

(90, 244, 129)-Net over F₄ — Digital

Digital (90, 244, 129)-net over F₄, using

t-expansion [i] based on digital (81, 244, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(90, 244, 733)-Net in Base 4 — Upper bound on s

There is no (90, 244, 734)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 867 744095 930183 910026 608879 542943 111745 895807 991431 243131 406297 721187 080003 076671 827864 891397 838453 131108 612509 207928 179445 340307 467590 468337 108335 > 4²⁴⁴ [i]