Best Known (107, 107+54, s)-Nets in Base 8
(107, 107+54, 402)-Net over F8 — Constructive and digital
Digital (107, 161, 402)-net over F8, using
- 1 times m-reduction [i] based on digital (107, 162, 402)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 38, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (69, 124, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 62, 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, 62, 177)-net over F64, using
- digital (11, 38, 48)-net over F8, using
- (u, u+v)-construction [i] based on
(107, 107+54, 576)-Net in Base 8 — Constructive
(107, 161, 576)-net in base 8, using
- t-expansion [i] based on (105, 161, 576)-net in base 8, using
- 7 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
- trace code for nets [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
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
- 7 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
(107, 107+54, 1656)-Net over F8 — Digital
Digital (107, 161, 1656)-net over F8, using
(107, 107+54, 378775)-Net in Base 8 — Upper bound on s
There is no (107, 161, 378776)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 24 975395 154904 685219 615561 920088 309013 374730 944827 815533 163242 553521 061132 154386 782995 443391 658034 551599 899015 926704 848237 918270 435556 774263 722000 > 8161 [i]