Best Known (114−68, 114, s)-Nets in Base 9
(114−68, 114, 81)-Net over F9 — Constructive and digital
Digital (46, 114, 81)-net over F9, using
- t-expansion [i] based on digital (32, 114, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(114−68, 114, 84)-Net in Base 9 — Constructive
(46, 114, 84)-net in base 9, using
- base change [i] based on digital (8, 76, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(114−68, 114, 162)-Net over F9 — Digital
Digital (46, 114, 162)-net over F9, using
- net from sequence [i] based on digital (46, 161)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 46 and N(F) ≥ 162, using
(114−68, 114, 2657)-Net in Base 9 — Upper bound on s
There is no (46, 114, 2658)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6 085953 600273 008979 412520 380472 350393 567860 326233 726502 459394 663293 600049 543130 042230 269050 974341 997016 541409 > 9114 [i]