MinT - Best Known (199−78, 199, s)-Nets in Base 4

Best Known (199−78, 199, s)-Nets in Base 4

(199−78, 199, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(199−78, 199, 311)-Net over F₄ — Digital

Digital (121, 199, 311)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−78, 199, 6026)-Net in Base 4 — Upper bound on s

There is no (121, 199, 6027)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 648037 817904 181121 981215 552502 987317 287681 246975 754565 966123 314235 181184 408541 162606 211630 961378 662340 333956 297694 150528 > 4¹⁹⁹ [i]