Best Known (130, 130+37, s)-Nets in Base 4
(130, 130+37, 1044)-Net over F4 — Constructive and digital
Digital (130, 167, 1044)-net over F4, using
- 1 times m-reduction [i] based on digital (130, 168, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 42, 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, 42, 261)-net over F256, using
(130, 130+37, 3296)-Net over F4 — Digital
Digital (130, 167, 3296)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4167, 3296, F4, 37) (dual of [3296, 3129, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4167, 4113, F4, 37) (dual of [4113, 3946, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(32) [i] based on
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(36) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(4167, 4113, F4, 37) (dual of [4113, 3946, 38]-code), using
(130, 130+37, 898116)-Net in Base 4 — Upper bound on s
There is no (130, 167, 898117)-net in base 4, because
- 1 times m-reduction [i] would yield (130, 166, 898117)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 8749 037509 191980 130714 352752 651730 132679 618182 750019 482789 068708 240222 817056 813822 814105 226958 898216 > 4166 [i]