Best Known (66, 66+42, s)-Nets in Base 8
(66, 66+42, 354)-Net over F8 — Constructive and digital
Digital (66, 108, 354)-net over F8, using
- 10 times m-reduction [i] based on digital (66, 118, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 59, 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, 59, 177)-net over F64, using
(66, 66+42, 384)-Net in Base 8 — Constructive
(66, 108, 384)-net in base 8, using
- 2 times m-reduction [i] based on (66, 110, 384)-net in base 8, using
- trace code for nets [i] based on (11, 55, 192)-net in base 64, using
- 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 48, 192)-net over F128, using
- 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- trace code for nets [i] based on (11, 55, 192)-net in base 64, using
(66, 66+42, 565)-Net over F8 — Digital
Digital (66, 108, 565)-net over F8, using
(66, 66+42, 54670)-Net in Base 8 — Upper bound on s
There is no (66, 108, 54671)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 34 180667 171776 120619 858058 954782 523294 160843 495131 801453 532842 857876 390678 232599 920753 017138 983568 > 8108 [i]