Best Known (128, 128+127, s)-Nets in Base 4
(128, 128+127, 130)-Net over F4 — Constructive and digital
Digital (128, 255, 130)-net over F4, using
- t-expansion [i] based on digital (105, 255, 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
(128, 128+127, 181)-Net over F4 — Digital
Digital (128, 255, 181)-net over F4, using
(128, 128+127, 2115)-Net in Base 4 — Upper bound on s
There is no (128, 255, 2116)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 254, 2116)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 845 661878 966010 353311 832854 308279 822802 382017 796613 925986 142345 495133 549614 200916 361285 549987 432290 966374 435626 436589 735963 920132 096951 216761 185856 158960 > 4254 [i]