Best Known (121, 155, s)-Nets in Base 4
(121, 155, 1044)-Net over F4 — Constructive and digital
Digital (121, 155, 1044)-net over F4, using
- 1 times m-reduction [i] based on digital (121, 156, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 39, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 39, 261)-net over F256, using
(121, 155, 3341)-Net over F4 — Digital
Digital (121, 155, 3341)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4155, 3341, F4, 34) (dual of [3341, 3186, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4155, 4113, F4, 34) (dual of [4113, 3958, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- linear OA(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(4155, 4113, F4, 34) (dual of [4113, 3958, 35]-code), using
(121, 155, 738221)-Net in Base 4 — Upper bound on s
There is no (121, 155, 738222)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2085 970754 925077 213941 898538 301023 939565 051707 940461 757237 981235 632851 280672 648969 671504 947110 > 4155 [i]