MinT - Best Known (89, 184, s)-Nets in Base 4

Best Known (89, 184, s)-Nets in Base 4

(89, 184, 104)-Net over F₄ — Constructive and digital

Digital (89, 184, 104)-net over F₄, using

t-expansion [i] based on digital (73, 184, 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]

(89, 184, 129)-Net over F₄ — Digital

Digital (89, 184, 129)-net over F₄, using

t-expansion [i] based on digital (81, 184, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(89, 184, 1314)-Net in Base 4 — Upper bound on s

There is no (89, 184, 1315)-net in base 4, because

1 times m-reduction [i] would yield (89, 183, 1315)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153 744524 318947 545927 073963 769582 138271 707228 753705 865113 038287 899979 588564 744876 992652 153065 544634 505283 051520 > 4¹⁸³ [i]