Best Known (93, 93+63, s)-Nets in Base 8
(93, 93+63, 354)-Net over F8 — Constructive and digital
Digital (93, 156, 354)-net over F8, using
- 16 times m-reduction [i] based on digital (93, 172, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 86, 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, 86, 177)-net over F64, using
(93, 93+63, 384)-Net in Base 8 — Constructive
(93, 156, 384)-net in base 8, using
- 82 times duplication [i] based on (91, 154, 384)-net in base 8, using
- trace code for nets [i] based on (14, 77, 192)-net in base 64, using
- base change [i] based on digital (3, 66, 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, 66, 192)-net over F128, using
- trace code for nets [i] based on (14, 77, 192)-net in base 64, using
(93, 93+63, 632)-Net over F8 — Digital
Digital (93, 156, 632)-net over F8, using
(93, 93+63, 58108)-Net in Base 8 — Upper bound on s
There is no (93, 156, 58109)-net in base 8, because
- 1 times m-reduction [i] would yield (93, 155, 58109)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 95 293453 809706 911169 028598 933668 817840 173021 103176 084249 969359 532563 601514 344423 499275 768204 264476 068014 411920 428400 505998 287291 102254 066400 > 8155 [i]