Best Known (84, 84+56, s)-Nets in Base 5
(84, 84+56, 252)-Net over F5 — Constructive and digital
Digital (84, 140, 252)-net over F5, using
- 8 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+56, 302)-Net over F5 — Digital
Digital (84, 140, 302)-net over F5, using
(84, 84+56, 8806)-Net in Base 5 — Upper bound on s
There is no (84, 140, 8807)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 71 940221 685670 299124 836576 341209 100543 440765 370732 204458 838841 804475 870014 423474 660514 272030 379665 > 5140 [i]