Best Known (217−106, 217, s)-Nets in Base 4
(217−106, 217, 130)-Net over F4 — Constructive and digital
Digital (111, 217, 130)-net over F4, using
- t-expansion [i] based on digital (105, 217, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(217−106, 217, 166)-Net over F4 — Digital
Digital (111, 217, 166)-net over F4, using
(217−106, 217, 1959)-Net in Base 4 — Upper bound on s
There is no (111, 217, 1960)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 44577 702678 881523 287557 611181 376390 104080 301613 815869 727351 549776 082985 453041 166390 384661 638168 669764 501917 156278 123302 081980 472360 > 4217 [i]