Best Known (72, 72+78, s)-Nets in Base 9
(72, 72+78, 165)-Net over F9 — Constructive and digital
Digital (72, 150, 165)-net over F9, using
- t-expansion [i] based on digital (64, 150, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(72, 72+78, 234)-Net over F9 — Digital
Digital (72, 150, 234)-net over F9, using
(72, 72+78, 8981)-Net in Base 9 — Upper bound on s
There is no (72, 150, 8982)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 137214 542090 660360 449619 615176 715028 040480 666417 383765 121667 989473 033689 488041 701126 459179 858515 964547 856340 535328 808637 860001 186179 820148 066065 > 9150 [i]