Best Known (128, 128+123, s)-Nets in Base 4
(128, 128+123, 130)-Net over F4 — Constructive and digital
Digital (128, 251, 130)-net over F4, using
- t-expansion [i] based on digital (105, 251, 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+123, 187)-Net over F4 — Digital
Digital (128, 251, 187)-net over F4, using
(128, 128+123, 2254)-Net in Base 4 — Upper bound on s
There is no (128, 251, 2255)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 250, 2255)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 318009 442646 711302 219574 037486 282678 620740 404420 188183 329218 946877 063695 899649 967790 560695 220195 698151 599107 135158 799439 962180 175954 039875 602249 373736 > 4250 [i]