MinT - Best Known (78, 78+138, s)-Nets in Base 4

Best Known (78, 78+138, s)-Nets in Base 4

(78, 78+138, 104)-Net over F₄ — Constructive and digital

Digital (78, 216, 104)-net over F₄, using

t-expansion [i] based on digital (73, 216, 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+138, 112)-Net over F₄ — Digital

Digital (78, 216, 112)-net over F₄, using

t-expansion [i] based on digital (73, 216, 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+138, 622)-Net in Base 4 — Upper bound on s

There is no (78, 216, 623)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11320 989886 922546 460019 953814 110707 655381 714585 182817 268723 836454 284248 702660 356416 967808 835629 062539 179545 999687 916789 546786 235526 > 4²¹⁶ [i]