Best Known (82, 128, s)-Nets in Base 5
(82, 128, 252)-Net over F5 — Constructive and digital
Digital (82, 128, 252)-net over F5, using
- 16 times m-reduction [i] based on digital (82, 144, 252)-net over F5, using
- trace code for nets [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
- trace code for nets [i] based on digital (10, 72, 126)-net over F25, using
(82, 128, 423)-Net over F5 — Digital
Digital (82, 128, 423)-net over F5, using
(82, 128, 18277)-Net in Base 5 — Upper bound on s
There is no (82, 128, 18278)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 294029 820214 700570 194588 756472 287178 728474 913162 600095 249554 818849 773056 317455 076500 612025 > 5128 [i]