MinT - Best Known (195−77, 195, s)-Nets in Base 4

Best Known (195−77, 195, s)-Nets in Base 4

(195−77, 195, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(195−77, 195, 298)-Net over F₄ — Digital

Digital (118, 195, 298)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−77, 195, 5903)-Net in Base 4 — Upper bound on s

There is no (118, 195, 5904)-net in base 4, because

1 times m-reduction [i] would yield (118, 194, 5904)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 634 401312 713888 773441 508991 405444 975693 783107 388390 024672 047309 569606 272968 064902 247277 464320 363434 259937 208859 333704 > 4¹⁹⁴ [i]