MinT - Best Known (78, 78+166, s)-Nets in Base 4

Best Known (78, 78+166, s)-Nets in Base 4

(78, 78+166, 104)-Net over F₄ — Constructive and digital

Digital (78, 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]

(78, 78+166, 112)-Net over F₄ — Digital

Digital (78, 244, 112)-net over F₄, using

t-expansion [i] based on digital (73, 244, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(78, 78+166, 556)-Net in Base 4 — Upper bound on s

There is no (78, 244, 557)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 878 627343 924996 276156 742845 414656 386412 472449 685782 943973 623168 002847 030024 750989 703074 384607 722215 899443 251440 254050 383872 027872 085837 618502 940480 > 4²⁴⁴ [i]