MinT - Best Known (195−83, 195, s)-Nets in Base 4

Best Known (195−83, 195, s)-Nets in Base 4

(195−83, 195, 130)-Net over F₄ — Constructive and digital

Digital (112, 195, 130)-net over F₄, using

t-expansion [i] based on digital (105, 195, 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]

(195−83, 195, 234)-Net over F₄ — Digital

Digital (112, 195, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−83, 195, 3764)-Net in Base 4 — Upper bound on s

There is no (112, 195, 3765)-net in base 4, because

1 times m-reduction [i] would yield (112, 194, 3765)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 633 705629 488254 612947 646123 792209 782152 481049 463036 825530 439172 930998 109129 468170 945363 203043 355980 662852 826994 170160 > 4¹⁹⁴ [i]