Best Known (110, 151, s)-Nets in Base 4
(110, 151, 531)-Net over F4 — Constructive and digital
Digital (110, 151, 531)-net over F4, using
- t-expansion [i] based on digital (109, 151, 531)-net over F4, using
- 2 times m-reduction [i] based on digital (109, 153, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 51, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 51, 177)-net over F64, using
- 2 times m-reduction [i] based on digital (109, 153, 531)-net over F4, using
(110, 151, 1025)-Net over F4 — Digital
Digital (110, 151, 1025)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4151, 1025, F4, 41) (dual of [1025, 874, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
(110, 151, 90689)-Net in Base 4 — Upper bound on s
There is no (110, 151, 90690)-net in base 4, because
- 1 times m-reduction [i] would yield (110, 150, 90690)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 037213 957901 657995 440274 469417 456559 424513 868435 011468 544374 045074 933190 937052 226402 012976 > 4150 [i]