MinT - Best Known (105, 105+63, s)-Nets in Base 4

Best Known (105, 105+63, s)-Nets in Base 4

(105, 105+63, 130)-Net over F₄ — Constructive and digital

Digital (105, 168, 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+63, 314)-Net over F₄ — Digital

Digital (105, 168, 314)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+63, 7223)-Net in Base 4 — Upper bound on s

There is no (105, 168, 7224)-net in base 4, because

1 times m-reduction [i] would yield (105, 167, 7224)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35068 259414 757184 734803 406641 366393 039332 563785 103652 996644 608683 116279 463766 822610 520757 737456 689484 > 4¹⁶⁷ [i]