Best Known (79, 79+57, s)-Nets in Base 5
(79, 79+57, 252)-Net over F5 — Constructive and digital
Digital (79, 136, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (79, 138, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 69, 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
- trace code for nets [i] based on digital (10, 69, 126)-net over F25, using
(79, 79+57, 6601)-Net in Base 5 — Upper bound on s
There is no (79, 136, 6602)-net in base 5, because
- 1 times m-reduction [i] would yield (79, 135, 6602)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 23020 368740 897613 038767 719234 949773 042683 194028 569870 993264 012974 521615 371817 116197 087380 882625 > 5135 [i]