Best Known (128, 128+129, s)-Nets in Base 4
(128, 128+129, 130)-Net over F4 — Constructive and digital
Digital (128, 257, 130)-net over F4, using
- t-expansion [i] based on digital (105, 257, 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+129, 178)-Net over F4 — Digital
Digital (128, 257, 178)-net over F4, using
(128, 128+129, 2053)-Net in Base 4 — Upper bound on s
There is no (128, 257, 2054)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 256, 2054)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13743 050982 758306 122883 537527 477926 535308 845191 137290 793087 859769 633775 755728 660892 497595 719381 653148 177313 652760 579487 588243 898483 270240 152027 688477 817312 > 4256 [i]