MinT - Best Known (170−92, 170, s)-Nets in Base 4

Best Known (170−92, 170, s)-Nets in Base 4

(170−92, 170, 104)-Net over F₄ — Constructive and digital

Digital (78, 170, 104)-net over F₄, using

t-expansion [i] based on digital (73, 170, 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]

(170−92, 170, 112)-Net over F₄ — Digital

Digital (78, 170, 112)-net over F₄, using

t-expansion [i] based on digital (73, 170, 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]

(170−92, 170, 969)-Net in Base 4 — Upper bound on s

There is no (78, 170, 970)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 250670 949274 622906 352281 918619 302304 209740 281260 043900 830866 798076 784896 023967 553222 058905 577515 177632 > 4¹⁷⁰ [i]