MinT - Best Known (99, 99+135, s)-Nets in Base 4

Best Known (99, 99+135, s)-Nets in Base 4

(99, 99+135, 104)-Net over F₄ — Constructive and digital

Digital (99, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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+135, 144)-Net over F₄ — Digital

Digital (99, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 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+135, 1012)-Net in Base 4 — Upper bound on s

There is no (99, 234, 1013)-net in base 4, because

1 times m-reduction [i] would yield (99, 233, 1013)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 284363 704567 655379 026746 735052 801904 033812 525659 956066 915036 491536 535751 928347 768011 913907 948869 735275 213468 048693 495607 113596 178559 466980 > 4²³³ [i]