MinT - Best Known (116, 116+72, s)-Nets in Base 4

Best Known (116, 116+72, s)-Nets in Base 4

(116, 116+72, 130)-Net over F₄ — Constructive and digital

Digital (116, 188, 130)-net over F₄, using

t-expansion [i] based on 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]

(116, 116+72, 321)-Net over F₄ — Digital

Digital (116, 188, 321)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+72, 6603)-Net in Base 4 — Upper bound on s

There is no (116, 188, 6604)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 154329 891036 639998 687801 636214 993906 685022 913829 818338 562123 304024 513246 112760 502823 983882 776586 398804 537270 949828 > 4¹⁸⁸ [i]