Best Known (107, 107+30, s)-Nets in Base 4
(107, 107+30, 1044)-Net over F4 — Constructive and digital
Digital (107, 137, 1044)-net over F4, using
- 41 times duplication [i] based on digital (106, 136, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 34, 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, 34, 261)-net over F256, using
(107, 107+30, 3142)-Net over F4 — Digital
Digital (107, 137, 3142)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4137, 3142, F4, 30) (dual of [3142, 3005, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4137, 4113, F4, 30) (dual of [4113, 3976, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- 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(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(29) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4137, 4113, F4, 30) (dual of [4113, 3976, 31]-code), using
(107, 107+30, 675230)-Net in Base 4 — Upper bound on s
There is no (107, 137, 675231)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 30354 324283 717443 879293 493791 014555 320944 477169 961700 337682 591386 028465 309817 542948 > 4137 [i]