MinT - Best Known (186−71, 186, s)-Nets in Base 4

Best Known (186−71, 186, s)-Nets in Base 4

(186−71, 186, 130)-Net over F₄ — Constructive and digital

Digital (115, 186, 130)-net over F₄, using

t-expansion [i] based on digital (105, 186, 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]

(186−71, 186, 321)-Net over F₄ — Digital

Digital (115, 186, 321)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−71, 186, 7025)-Net in Base 4 — Upper bound on s

There is no (115, 186, 7026)-net in base 4, because

1 times m-reduction [i] would yield (115, 185, 7026)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2407 645635 177338 680306 877169 335591 135943 284346 024140 943956 903469 053819 566327 995588 652618 211353 723101 676142 690632 > 4¹⁸⁵ [i]