Best Known (97, 97+42, s)-Nets in Base 8
(97, 97+42, 513)-Net over F8 — Constructive and digital
Digital (97, 139, 513)-net over F8, using
- base reduction for projective spaces (embedding PG(69,64) in PG(138,8)) for nets [i] based on digital (28, 70, 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
(97, 97+42, 576)-Net in Base 8 — Constructive
(97, 139, 576)-net in base 8, using
- 15 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
- trace code for nets [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
- trace code for nets [i] based on (20, 77, 288)-net in base 64, using
(97, 97+42, 2678)-Net over F8 — Digital
Digital (97, 139, 2678)-net over F8, using
(97, 97+42, 1177566)-Net in Base 8 — Upper bound on s
There is no (97, 139, 1177567)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 338465 002846 242121 335321 287422 856582 176098 743211 522075 541771 354780 949202 196923 848568 037061 828726 689456 715657 719388 236255 554050 > 8139 [i]