Best Known (105−38, 105, s)-Nets in Base 5
(105−38, 105, 252)-Net over F5 — Constructive and digital
Digital (67, 105, 252)-net over F5, using
- 9 times m-reduction [i] based on digital (67, 114, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 57, 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, 57, 126)-net over F25, using
(105−38, 105, 352)-Net over F5 — Digital
Digital (67, 105, 352)-net over F5, using
(105−38, 105, 14436)-Net in Base 5 — Upper bound on s
There is no (67, 105, 14437)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 24 658115 250156 657369 335549 551164 117040 185425 488797 781425 506102 695643 302925 > 5105 [i]