MinT - Best Known (99, 99+112, s)-Nets in Base 4

Best Known (99, 99+112, s)-Nets in Base 4

(99, 99+112, 104)-Net over F₄ — Constructive and digital

Digital (99, 211, 104)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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, 99+112, 144)-Net over F₄ — Digital

Digital (99, 211, 144)-net over F₄, using

t-expansion [i] based on digital (91, 211, 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, 99+112, 1297)-Net in Base 4 — Upper bound on s

There is no (99, 211, 1298)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 207711 466742 071666 417289 042135 709621 353249 632587 222482 929689 882936 817154 547098 258093 453770 958193 380797 033366 714469 531335 282400 > 4²¹¹ [i]