MinT - Best Known (170−96, 170, s)-Nets in Base 4

Best Known (170−96, 170, s)-Nets in Base 4

(170−96, 170, 104)-Net over F₄ — Constructive and digital

Digital (74, 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]

(170−96, 170, 112)-Net over F₄ — Digital

Digital (74, 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]

(170−96, 170, 808)-Net in Base 4 — Upper bound on s

There is no (74, 170, 809)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 324363 286758 807468 340491 017755 500828 109684 720195 179294 102815 458926 229689 486701 989465 530544 609826 334800 > 4¹⁷⁰ [i]