Best Known (11, 11+55, s)-Nets in Base 25
(11, 11+55, 126)-Net over F25 — Constructive and digital
Digital (11, 66, 126)-net over F25, using
- t-expansion [i] based on digital (10, 66, 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, 11+55, 1041)-Net in Base 25 — Upper bound on s
There is no (11, 66, 1042)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 65, 1042)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 7 388507 860903 539938 842773 397426 362157 912627 392194 421673 706312 976164 886972 465380 055562 013905 > 2565 [i]