Best Known (84, 84+52, s)-Nets in Base 5
(84, 84+52, 252)-Net over F5 — Constructive and digital
Digital (84, 136, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (84, 148, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 74, 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, 74, 126)-net over F25, using
(84, 84+52, 348)-Net over F5 — Digital
Digital (84, 136, 348)-net over F5, using
(84, 84+52, 11931)-Net in Base 5 — Upper bound on s
There is no (84, 136, 11932)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 114931 985447 509634 310396 459956 230677 102150 112983 430280 416716 228232 233771 378216 876919 778095 757377 > 5136 [i]