Best Known (72−59, 72, s)-Nets in Base 25
(72−59, 72, 126)-Net over F25 — Constructive and digital
Digital (13, 72, 126)-net over F25, using
- t-expansion [i] based on digital (10, 72, 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
(72−59, 72, 1271)-Net in Base 25 — Upper bound on s
There is no (13, 72, 1272)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 71, 1272)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1815 534991 479443 210580 014472 602215 817281 522751 821119 412785 580081 317951 714643 125575 542828 590940 482625 > 2571 [i]