MinT - Best Known (125, 125+125, s)-Nets in Base 4

Best Known (125, 125+125, s)-Nets in Base 4

(125, 125+125, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(125, 125+125, 176)-Net over F₄ — Digital

Digital (125, 250, 176)-net over F₄, using

net from sequence [i] based on digital (125, 175)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
  - Drinfeld modules of rank 1 [i]

(125, 125+125, 2037)-Net in Base 4 — Upper bound on s

There is no (125, 250, 2038)-net in base 4, because

1 times m-reduction [i] would yield (125, 249, 2038)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 823870 420099 178229 141425 674030 950836 181257 691742 198501 246839 181487 706597 035294 014077 197940 523302 678942 930765 719485 684004 045980 359695 019153 912358 183840 > 4²⁴⁹ [i]