MinT - Best Known (99, 99+137, s)-Nets in Base 4

Best Known (99, 99+137, s)-Nets in Base 4

(99, 99+137, 104)-Net over F₄ — Constructive and digital

Digital (99, 236, 104)-net over F₄, using

t-expansion [i] based on digital (73, 236, 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+137, 144)-Net over F₄ — Digital

Digital (99, 236, 144)-net over F₄, using

t-expansion [i] based on digital (91, 236, 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+137, 994)-Net in Base 4 — Upper bound on s

There is no (99, 236, 995)-net in base 4, because

1 times m-reduction [i] would yield (99, 235, 995)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3105 244613 613543 043041 420125 240214 751411 863937 813546 676251 643456 981167 797058 712539 382467 983053 560030 397626 209473 789408 358972 384596 893158 589192 > 4²³⁵ [i]