Best Known (100, 100+52, s)-Nets in Base 8
(100, 100+52, 389)-Net over F8 — Constructive and digital
Digital (100, 152, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 34, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- 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
- digital (8, 34, 35)-net over F8, using
(100, 100+52, 576)-Net in Base 8 — Constructive
(100, 152, 576)-net in base 8, using
- 6 times m-reduction [i] based on (100, 158, 576)-net in base 8, using
- trace code for nets [i] based on (21, 79, 288)-net in base 64, using
- 5 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
- 5 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- trace code for nets [i] based on (21, 79, 288)-net in base 64, using
(100, 100+52, 1420)-Net over F8 — Digital
Digital (100, 152, 1420)-net over F8, using
(100, 100+52, 286928)-Net in Base 8 — Upper bound on s
There is no (100, 152, 286929)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 186081 687677 571031 481170 775748 053488 488680 346017 454138 869698 059305 640879 313386 759341 413872 662509 895093 151057 760413 370372 059232 103258 732128 > 8152 [i]