MinT - Best Known (188−83, 188, s)-Nets in Base 4

Best Known (188−83, 188, s)-Nets in Base 4

(188−83, 188, 130)-Net over F₄ — Constructive and digital

Digital (105, 188, 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]

(188−83, 188, 202)-Net over F₄ — Digital

Digital (105, 188, 202)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−83, 188, 2964)-Net in Base 4 — Upper bound on s

There is no (105, 188, 2965)-net in base 4, because

1 times m-reduction [i] would yield (105, 187, 2965)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38971 147886 316490 005651 727048 102159 702146 746774 479041 184558 810836 048167 156814 136310 760292 213950 899644 024108 225600 > 4¹⁸⁷ [i]