Best Known (12, 12+64, s)-Nets in Base 81
(12, 12+64, 172)-Net over F81 — Constructive and digital
Digital (12, 76, 172)-net over F81, using
- t-expansion [i] based on digital (7, 76, 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
(12, 12+64, 298)-Net over F81 — Digital
Digital (12, 76, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
(12, 12+64, 5434)-Net in Base 81 — Upper bound on s
There is no (12, 76, 5435)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 11 108817 690987 626026 841091 061029 354431 830994 703838 955525 039242 744039 333890 659838 576699 023729 448496 623343 599582 987557 018512 096531 840556 054770 265601 > 8176 [i]