Best Known (131, 131+115, s)-Nets in Base 4
(131, 131+115, 130)-Net over F4 — Constructive and digital
Digital (131, 246, 130)-net over F4, using
- t-expansion [i] based on digital (105, 246, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction 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]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(131, 131+115, 214)-Net over F4 — Digital
Digital (131, 246, 214)-net over F4, using
(131, 131+115, 2802)-Net in Base 4 — Upper bound on s
There is no (131, 246, 2803)-net in base 4, because
- 1 times m-reduction [i] would yield (131, 245, 2803)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3249 174935 218995 529238 941181 651744 931267 092060 586041 640835 038537 270671 664325 611678 940608 460301 527437 865918 537819 055913 859715 090408 330963 529301 992016 > 4245 [i]