MinT - Best Known (105, 105+81, s)-Nets in Base 4

Best Known (105, 105+81, s)-Nets in Base 4

(105, 105+81, 130)-Net over F₄ — Constructive and digital

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]

(105, 105+81, 209)-Net over F₄ — Digital

Digital (105, 186, 209)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+81, 3167)-Net in Base 4 — Upper bound on s

There is no (105, 186, 3168)-net in base 4, because

1 times m-reduction [i] would yield (105, 185, 3168)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2415 630998 188896 972709 083660 570805 756417 360695 904101 007682 547317 584121 359064 815196 706323 712011 267582 965069 323874 > 4¹⁸⁵ [i]