Best Known (78−66, 78, s)-Nets in Base 25
(78−66, 78, 126)-Net over F25 — Constructive and digital
Digital (12, 78, 126)-net over F25, using
- t-expansion [i] based on digital (10, 78, 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
(78−66, 78, 1087)-Net in Base 25 — Upper bound on s
There is no (12, 78, 1088)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 11 048553 524560 038732 068709 029981 731219 325218 430021 359435 119410 396751 267805 951238 651052 345730 553223 898720 740865 > 2578 [i]