Best Known (207−79, 207, s)-Nets in Base 3
(207−79, 207, 156)-Net over F3 — Constructive and digital
Digital (128, 207, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (128, 212, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 106, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the 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) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 106, 78)-net over F9, using
(207−79, 207, 220)-Net over F3 — Digital
Digital (128, 207, 220)-net over F3, using
(207−79, 207, 2511)-Net in Base 3 — Upper bound on s
There is no (128, 207, 2512)-net in base 3, because
- 1 times m-reduction [i] would yield (128, 206, 2512)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 193 809103 081686 729991 817323 618316 097895 197374 885289 972487 279917 909733 578483 994904 542718 930852 190657 > 3206 [i]