Best Known (84−20, 84, s)-Nets in Base 7
(84−20, 84, 688)-Net over F7 — Constructive and digital
Digital (64, 84, 688)-net over F7, using
- 2 times m-reduction [i] based on digital (64, 86, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 43, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- trace code for nets [i] based on digital (21, 43, 344)-net over F49, using
(84−20, 84, 7209)-Net over F7 — Digital
Digital (64, 84, 7209)-net over F7, using
(84−20, 84, large)-Net in Base 7 — Upper bound on s
There is no (64, 84, large)-net in base 7, because
- 18 times m-reduction [i] would yield (64, 66, large)-net in base 7, but