MinT - Best Known (246−139, 246, s)-Nets in Base 4

Best Known (246−139, 246, s)-Nets in Base 4

(246−139, 246, 130)-Net over F₄ — Constructive and digital

Digital (107, 246, 130)-net over F₄, using

t-expansion [i] based on digital (105, 246, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(246−139, 246, 144)-Net over F₄ — Digital

Digital (107, 246, 144)-net over F₄, using

t-expansion [i] based on digital (91, 246, 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]

(246−139, 246, 1158)-Net in Base 4 — Upper bound on s

There is no (107, 246, 1159)-net in base 4, because

1 times m-reduction [i] would yield (107, 245, 1159)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3341 299885 079263 029874 573223 552805 095610 070472 077743 189735 999250 092774 233748 411495 768797 307840 282086 829365 717605 799996 388444 316820 587458 294865 157140 > 4²⁴⁵ [i]