MinT - Best Known (71, 71+75, s)-Nets in Base 4

Best Known (71, 71+75, s)-Nets in Base 4

(71, 71+75, 66)-Net over F₄ — Constructive and digital

Digital (71, 146, 66)-net over F₄, using

t-expansion [i] based on digital (49, 146, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(71, 71+75, 105)-Net over F₄ — Digital

Digital (71, 146, 105)-net over F₄, using

t-expansion [i] based on digital (70, 146, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(71, 71+75, 1087)-Net in Base 4 — Upper bound on s

There is no (71, 146, 1088)-net in base 4, because

1 times m-reduction [i] would yield (71, 145, 1088)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2029 615297 387376 600424 242220 048827 003583 280656 434893 063970 642694 004665 174327 273677 043187 > 4¹⁴⁵ [i]