MinT - Best Known (195−116, 195, s)-Nets in Base 4

Best Known (195−116, 195, s)-Nets in Base 4

(195−116, 195, 104)-Net over F₄ — Constructive and digital

Digital (79, 195, 104)-net over F₄, using

t-expansion [i] based on digital (73, 195, 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]

(195−116, 195, 112)-Net over F₄ — Digital

Digital (79, 195, 112)-net over F₄, using

t-expansion [i] based on digital (73, 195, 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]

(195−116, 195, 744)-Net in Base 4 — Upper bound on s

There is no (79, 195, 745)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2632 576316 982956 188557 240775 499515 658375 023885 252281 435772 495663 419472 779404 909971 509796 549349 140627 142338 025915 421088 > 4¹⁹⁵ [i]