Best Known (67, 67+134, s)-Nets in Base 4
(67, 67+134, 66)-Net over F4 — Constructive and digital
Digital (67, 201, 66)-net over F4, using
- t-expansion [i] based on digital (49, 201, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(67, 67+134, 99)-Net over F4 — Digital
Digital (67, 201, 99)-net over F4, using
- t-expansion [i] based on digital (61, 201, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(67, 67+134, 496)-Net in Base 4 — Upper bound on s
There is no (67, 201, 497)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10 620031 867463 183341 348305 808262 199740 248437 633276 210218 789491 348387 568193 549678 524892 637991 228157 695959 669295 627594 775760 > 4201 [i]