Best Known (128, 128+95, s)-Nets in Base 4
(128, 128+95, 130)-Net over F4 — Constructive and digital
Digital (128, 223, 130)-net over F4, using
- t-expansion [i] based on digital (105, 223, 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+95, 263)-Net over F4 — Digital
Digital (128, 223, 263)-net over F4, using
(128, 128+95, 4234)-Net in Base 4 — Upper bound on s
There is no (128, 223, 4235)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 222, 4235)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 45 606325 915153 758012 154519 385766 684944 220659 064606 616028 771366 727695 859481 021054 511064 155974 480793 477227 328945 286772 565242 774734 386944 > 4222 [i]