MinT - Best Known (170−90, 170, s)-Nets in Base 4

Best Known (170−90, 170, s)-Nets in Base 4

(170−90, 170, 104)-Net over F₄ — Constructive and digital

Digital (80, 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]

(170−90, 170, 112)-Net over F₄ — Digital

Digital (80, 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]

(170−90, 170, 1068)-Net in Base 4 — Upper bound on s

There is no (80, 170, 1069)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 256265 565165 479765 884259 154935 454564 517792 231923 247316 679632 842655 085600 474446 105842 982872 213963 709300 > 4¹⁷⁰ [i]