Best Known (80−50, 80, s)-Nets in Base 81
(80−50, 80, 370)-Net over F81 — Constructive and digital
Digital (30, 80, 370)-net over F81, using
- t-expansion [i] based on digital (16, 80, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(80−50, 80, 551)-Net over F81 — Digital
Digital (30, 80, 551)-net over F81, using
- net from sequence [i] based on digital (30, 550)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 30 and N(F) ≥ 551, using
(80−50, 80, 162800)-Net in Base 81 — Upper bound on s
There is no (30, 80, 162801)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 477 366337 690856 986867 495811 037510 973960 087503 800344 387508 007539 036852 141678 909200 299445 793140 242837 952540 983938 861808 119700 660704 128052 316084 696417 122001 > 8180 [i]