Best Known (65−57, 65, s)-Nets in Base 81
(65−57, 65, 172)-Net over F81 — Constructive and digital
Digital (8, 65, 172)-net over F81, using
- t-expansion [i] based on digital (7, 65, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(65−57, 65, 226)-Net over F81 — Digital
Digital (8, 65, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
(65−57, 65, 3238)-Net in Base 81 — Upper bound on s
There is no (8, 65, 3239)-net in base 81, because
- 1 times m-reduction [i] would yield (8, 64, 3239)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 139 871383 396789 547428 431587 412530 555603 498002 594439 535379 943591 133917 267374 377083 563205 313465 900677 756888 786394 585036 631361 > 8164 [i]