Best Known (135−36, 135, s)-Nets in Base 4
(135−36, 135, 531)-Net over F4 — Constructive and digital
Digital (99, 135, 531)-net over F4, using
- 3 times m-reduction [i] based on digital (99, 138, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 46, 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, 46, 177)-net over F64, using
(135−36, 135, 1023)-Net over F4 — Digital
Digital (99, 135, 1023)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4135, 1023, F4, 36) (dual of [1023, 888, 37]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
(135−36, 135, 82486)-Net in Base 4 — Upper bound on s
There is no (99, 135, 82487)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1897 381564 307546 774492 043704 659400 936698 147893 454054 046723 254196 542814 943499 670485 > 4135 [i]