MinT - Best Known (250−135, 250, s)-Nets in Base 4

Best Known (250−135, 250, s)-Nets in Base 4

(250−135, 250, 130)-Net over F₄ — Constructive and digital

Digital (115, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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]

(250−135, 250, 168)-Net over F₄ — Digital

Digital (115, 250, 168)-net over F₄, using

net from sequence [i] based on digital (115, 167)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(250−135, 250, 1430)-Net in Base 4 — Upper bound on s

There is no (115, 250, 1431)-net in base 4, because

1 times m-reduction [i] would yield (115, 249, 1431)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 835309 926099 684521 641074 805307 355892 203260 694145 114727 401796 738993 927057 150706 988724 206000 779098 527450 640012 370218 515371 578710 107146 768782 323990 895744 > 4²⁴⁹ [i]