Best Known (84, 84+72, s)-Nets in Base 4
(84, 84+72, 130)-Net over F4 — Constructive and digital
Digital (84, 156, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 78, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(84, 84+72, 149)-Net over F4 — Digital
Digital (84, 156, 149)-net over F4, using
(84, 84+72, 1905)-Net in Base 4 — Upper bound on s
There is no (84, 156, 1906)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8491 836601 167033 275030 779220 824036 169448 946314 378765 381412 319291 599640 227438 963545 904187 741020 > 4156 [i]