Best Known (111, 111+45, s)-Nets in Base 8
(111, 111+45, 1026)-Net over F8 — Constructive and digital
Digital (111, 156, 1026)-net over F8, using
- 10 times m-reduction [i] based on digital (111, 166, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
(111, 111+45, 3946)-Net over F8 — Digital
Digital (111, 156, 3946)-net over F8, using
(111, 111+45, 2981483)-Net in Base 8 — Upper bound on s
There is no (111, 156, 2981484)-net in base 8, because
- 1 times m-reduction [i] would yield (111, 155, 2981484)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 95 268348 162112 745209 795211 798024 341414 571882 005786 024458 329239 492463 433151 640998 228824 805800 676367 110865 462904 856729 537584 399196 250839 486924 > 8155 [i]