Best Known (98, 98+29, s)-Nets in Base 4
(98, 98+29, 1036)-Net over F4 — Constructive and digital
Digital (98, 127, 1036)-net over F4, using
- 1 times m-reduction [i] based on digital (98, 128, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 32, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 32, 259)-net over F256, using
(98, 98+29, 2328)-Net over F4 — Digital
Digital (98, 127, 2328)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4127, 2328, F4, 29) (dual of [2328, 2201, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
(98, 98+29, 528283)-Net in Base 4 — Upper bound on s
There is no (98, 127, 528284)-net in base 4, because
- 1 times m-reduction [i] would yield (98, 126, 528284)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7237 059383 433640 946244 387405 782085 227414 957944 617916 010022 187229 848993 342300 > 4126 [i]