Best Known (134, 134+115, s)-Nets in Base 4
(134, 134+115, 130)-Net over F4 — Constructive and digital
Digital (134, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 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
(134, 134+115, 224)-Net over F4 — Digital
Digital (134, 249, 224)-net over F4, using
(134, 134+115, 3017)-Net in Base 4 — Upper bound on s
There is no (134, 249, 3018)-net in base 4, because
- 1 times m-reduction [i] would yield (134, 248, 3018)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 205351 321609 904007 412776 714256 263476 255226 039802 927221 694857 893490 571139 183327 808233 856233 983978 032523 181866 535277 196853 283427 301163 394654 275452 493604 > 4248 [i]