Best Known (3, 3+42, s)-Nets in Base 128
(3, 3+42, 192)-Net over F128 — Constructive and digital
Digital (3, 45, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
(3, 3+42, 2171)-Net in Base 128 — Upper bound on s
There is no (3, 45, 2172)-net in base 128, because
- 8 times m-reduction [i] would yield (3, 37, 2172)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 928513 331002 857474 701739 343991 977389 443122 453578 244687 314025 159262 341315 173321 > 12837 [i]