MinT - Best Known (99, 99+119, s)-Nets in Base 4

Best Known (99, 99+119, s)-Nets in Base 4

(99, 99+119, 104)-Net over F₄ — Constructive and digital

Digital (99, 218, 104)-net over F₄, using

t-expansion [i] based on digital (73, 218, 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+119, 144)-Net over F₄ — Digital

Digital (99, 218, 144)-net over F₄, using

t-expansion [i] based on digital (91, 218, 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+119, 1198)-Net in Base 4 — Upper bound on s

There is no (99, 218, 1199)-net in base 4, because

1 times m-reduction [i] would yield (99, 217, 1199)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46061 298096 529637 269093 129664 814231 204019 686524 085666 056638 317955 792729 270125 128510 100755 873815 195765 318362 427175 702001 381587 329792 > 4²¹⁷ [i]