Best Known (71−57, 71, s)-Nets in Base 25
(71−57, 71, 126)-Net over F25 — Constructive and digital
Digital (14, 71, 126)-net over F25, using
- t-expansion [i] based on digital (10, 71, 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
(71−57, 71, 130)-Net over F25 — Digital
Digital (14, 71, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(71−57, 71, 1456)-Net in Base 25 — Upper bound on s
There is no (14, 71, 1457)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 70, 1457)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 72 470943 318152 586503 894035 425116 615937 841107 820488 783731 009356 590017 444035 145385 791750 757214 097185 > 2570 [i]