MinT - Best Known (250−143, 250, s)-Nets in Base 4

Best Known (250−143, 250, s)-Nets in Base 4

(250−143, 250, 130)-Net over F₄ — Constructive and digital

Digital (107, 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]

(250−143, 250, 144)-Net over F₄ — Digital

Digital (107, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(250−143, 250, 1117)-Net in Base 4 — Upper bound on s

There is no (107, 250, 1118)-net in base 4, because

1 times m-reduction [i] would yield (107, 249, 1118)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 858603 501848 896641 259274 010596 619628 711630 909958 839756 741476 057872 601343 191996 694049 129731 986388 201248 258080 565777 617757 701223 589844 727144 764580 129460 > 4²⁴⁹ [i]