Best Known (77, 77+46, s)-Nets in Base 8
(77, 77+46, 354)-Net over F8 — Constructive and digital
Digital (77, 123, 354)-net over F8, using
- 17 times m-reduction [i] based on digital (77, 140, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 70, 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, 70, 177)-net over F64, using
(77, 77+46, 432)-Net in Base 8 — Constructive
(77, 123, 432)-net in base 8, using
- 3 times m-reduction [i] based on (77, 126, 432)-net in base 8, using
- trace code for nets [i] based on (14, 63, 216)-net in base 64, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- trace code for nets [i] based on (14, 63, 216)-net in base 64, using
(77, 77+46, 762)-Net over F8 — Digital
Digital (77, 123, 762)-net over F8, using
(77, 77+46, 90961)-Net in Base 8 — Upper bound on s
There is no (77, 123, 90962)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1202 566384 721655 377350 494899 737143 197033 279726 474984 295374 263118 432359 135239 555890 464558 864077 072993 178428 506144 > 8123 [i]