MinT - Best Known (99, 99+161, s)-Nets in Base 4

Best Known (99, 99+161, s)-Nets in Base 4

(99, 99+161, 104)-Net over F₄ — Constructive and digital

Digital (99, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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+161, 144)-Net over F₄ — Digital

Digital (99, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 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+161, 842)-Net in Base 4 — Upper bound on s

There is no (99, 260, 843)-net in base 4, because

1 times m-reduction [i] would yield (99, 259, 843)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 868260 113335 780361 031402 579489 877181 857006 544046 043775 325085 660785 844654 504602 780881 252645 922091 218607 039174 095962 902648 041892 413816 031134 253041 305543 595376 > 4²⁵⁹ [i]