MinT - Best Known (246−133, 246, s)-Nets in Base 4

Best Known (246−133, 246, s)-Nets in Base 4

(246−133, 246, 130)-Net over F₄ — Constructive and digital

Digital (113, 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]

(246−133, 246, 165)-Net over F₄ — Digital

Digital (113, 246, 165)-net over F₄, using

t-expansion [i] based on digital (109, 246, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(246−133, 246, 1401)-Net in Base 4 — Upper bound on s

There is no (113, 246, 1402)-net in base 4, because

1 times m-reduction [i] would yield (113, 245, 1402)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3292 909963 696199 444097 088035 800620 474847 069778 352868 301134 513567 954758 610621 268736 297036 445590 826251 271635 824742 648615 533566 371791 181459 763487 479260 > 4²⁴⁵ [i]