MinT - Best Known (205−95, 205, s)-Nets in Base 4

Best Known (205−95, 205, s)-Nets in Base 4

(205−95, 205, 130)-Net over F₄ — Constructive and digital

Digital (110, 205, 130)-net over F₄, using

t-expansion [i] based on digital (105, 205, 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]

(205−95, 205, 187)-Net over F₄ — Digital

Digital (110, 205, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−95, 205, 2474)-Net in Base 4 — Upper bound on s

There is no (110, 205, 2475)-net in base 4, because

1 times m-reduction [i] would yield (110, 204, 2475)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 667 818373 489523 649608 797987 084688 846058 111263 961041 547023 968013 243844 807248 811503 481537 627419 246611 829180 291272 015737 618688 > 4²⁰⁴ [i]