MinT - Best Known (165−86, 165, s)-Nets in Base 4

Best Known (165−86, 165, s)-Nets in Base 4

(165−86, 165, 104)-Net over F₄ — Constructive and digital

Digital (79, 165, 104)-net over F₄, using

t-expansion [i] based on digital (73, 165, 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]

(165−86, 165, 112)-Net over F₄ — Digital

Digital (79, 165, 112)-net over F₄, using

t-expansion [i] based on digital (73, 165, 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]

(165−86, 165, 1114)-Net in Base 4 — Upper bound on s

There is no (79, 165, 1115)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2207 199231 710474 941137 690788 699436 918610 945274 531101 088590 271658 110830 980218 845861 042791 655426 696360 > 4¹⁶⁵ [i]