MinT - Best Known (173−99, 173, s)-Nets in Base 4

Best Known (173−99, 173, s)-Nets in Base 4

(173−99, 173, 104)-Net over F₄ — Constructive and digital

Digital (74, 173, 104)-net over F₄, using

t-expansion [i] based on digital (73, 173, 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]

(173−99, 173, 112)-Net over F₄ — Digital

Digital (74, 173, 112)-net over F₄, using

t-expansion [i] based on digital (73, 173, 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]

(173−99, 173, 787)-Net in Base 4 — Upper bound on s

There is no (74, 173, 788)-net in base 4, because

1 times m-reduction [i] would yield (74, 172, 788)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 986240 945305 770405 799972 238752 541497 137334 459102 920338 156539 817802 947616 378807 861905 803841 418619 820152 > 4¹⁷² [i]