MinT - Best Known (94, 94+155, s)-Nets in Base 4

Best Known (94, 94+155, s)-Nets in Base 4

(94, 94+155, 104)-Net over F₄ — Constructive and digital

Digital (94, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(94, 94+155, 144)-Net over F₄ — Digital

Digital (94, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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]

(94, 94+155, 792)-Net in Base 4 — Upper bound on s

There is no (94, 249, 793)-net in base 4, because

1 times m-reduction [i] would yield (94, 248, 793)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 216227 075838 786471 514147 888591 625215 339098 167990 866668 192802 500717 525100 728686 055834 128278 548670 330685 963170 701675 116042 437907 264483 262670 762649 014144 > 4²⁴⁸ [i]