MinT - Best Known (216−120, 216, s)-Nets in Base 4

Best Known (216−120, 216, s)-Nets in Base 4

(216−120, 216, 104)-Net over F₄ — Constructive and digital

Digital (96, 216, 104)-net over F₄, using

t-expansion [i] based on digital (73, 216, 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]

(216−120, 216, 144)-Net over F₄ — Digital

Digital (96, 216, 144)-net over F₄, using

t-expansion [i] based on digital (91, 216, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(216−120, 216, 1087)-Net in Base 4 — Upper bound on s

There is no (96, 216, 1088)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11110 504533 143985 272325 599886 295864 321179 436869 596220 855588 526125 151120 742284 787382 720626 335597 057560 465018 611058 362900 890486 029055 > 4²¹⁶ [i]