MinT - Best Known (199−91, 199, s)-Nets in Base 4

Best Known (199−91, 199, s)-Nets in Base 4

(199−91, 199, 130)-Net over F₄ — Constructive and digital

Digital (108, 199, 130)-net over F₄, using

t-expansion [i] based on digital (105, 199, 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]

(199−91, 199, 189)-Net over F₄ — Digital

Digital (108, 199, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−91, 199, 2582)-Net in Base 4 — Upper bound on s

There is no (108, 199, 2583)-net in base 4, because

1 times m-reduction [i] would yield (108, 198, 2583)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 163953 620947 300610 641161 067770 707363 027589 492178 117655 438292 742269 952247 668738 805471 184338 206188 367615 351032 304781 684032 > 4¹⁹⁸ [i]