MinT - Best Known (103, 103+116, s)-Nets in Base 4

Best Known (103, 103+116, s)-Nets in Base 4

(103, 103+116, 104)-Net over F₄ — Constructive and digital

Digital (103, 219, 104)-net over F₄, using

t-expansion [i] based on digital (73, 219, 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]

(103, 103+116, 144)-Net over F₄ — Digital

Digital (103, 219, 144)-net over F₄, using

t-expansion [i] based on digital (91, 219, 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]

(103, 103+116, 1356)-Net in Base 4 — Upper bound on s

There is no (103, 219, 1357)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 713064 090165 042876 992987 764653 951265 421718 055649 418966 376791 241685 479593 057516 003859 772076 944037 882060 766689 599911 515201 122698 328776 > 4²¹⁹ [i]