Best Known (128, 128+59, s)-Nets in Base 4
(128, 128+59, 312)-Net over F4 — Constructive and digital
Digital (128, 187, 312)-net over F4, using
- 41 times duplication [i] based on digital (127, 186, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 62, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 62, 104)-net over F64, using
(128, 128+59, 640)-Net over F4 — Digital
Digital (128, 187, 640)-net over F4, using
(128, 128+59, 28256)-Net in Base 4 — Upper bound on s
There is no (128, 187, 28257)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 186, 28257)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 9619 972302 542331 826518 994919 678733 730728 712915 102517 367088 052698 311903 493685 103628 056647 429704 472057 894940 332416 > 4186 [i]