Best Known (54, 79, s)-Nets in Base 8
(54, 79, 378)-Net over F8 — Constructive and digital
Digital (54, 79, 378)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (39, 64, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 32, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 32, 177)-net over F64, using
- digital (3, 15, 24)-net over F8, using
(54, 79, 522)-Net in Base 8 — Constructive
(54, 79, 522)-net in base 8, using
- 1 times m-reduction [i] based on (54, 80, 522)-net in base 8, using
- base change [i] based on digital (34, 60, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 30, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 30, 261)-net over F256, using
- base change [i] based on digital (34, 60, 522)-net over F16, using
(54, 79, 1327)-Net over F8 — Digital
Digital (54, 79, 1327)-net over F8, using
(54, 79, 560199)-Net in Base 8 — Upper bound on s
There is no (54, 79, 560200)-net in base 8, because
- 1 times m-reduction [i] would yield (54, 78, 560200)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 27607 296759 343449 856446 572750 137891 745029 654691 607528 016551 836381 709816 > 878 [i]