Best Known (11, 82, s)-Nets in Base 25
(11, 82, 126)-Net over F25 — Constructive and digital
Digital (11, 82, 126)-net over F25, using
- t-expansion [i] based on digital (10, 82, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(11, 82, 977)-Net in Base 25 — Upper bound on s
There is no (11, 82, 978)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 81, 978)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 173005 246489 644718 860234 350145 407219 595076 601435 228588 575384 150042 487383 681913 077767 946547 751078 067603 181035 489105 > 2581 [i]