MinT - Best Known (99, 225, s)-Nets in Base 4

Best Known (99, 225, s)-Nets in Base 4

(99, 225, 104)-Net over F₄ — Constructive and digital

Digital (99, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(99, 225, 144)-Net over F₄ — Digital

Digital (99, 225, 144)-net over F₄, using

t-expansion [i] based on digital (91, 225, 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]

(99, 225, 1093)-Net in Base 4 — Upper bound on s

There is no (99, 225, 1094)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2944 380647 781104 243317 721498 140605 162673 674843 570464 080966 510005 921410 920264 167885 524731 649443 630518 578351 445381 069132 355245 877403 203360 > 4²²⁵ [i]