Best Known (98, 98+28, s)-Nets in Base 4
(98, 98+28, 1040)-Net over F4 — Constructive and digital
Digital (98, 126, 1040)-net over F4, using
- 42 times duplication [i] based on digital (96, 124, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 31, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 31, 260)-net over F256, using
(98, 98+28, 2738)-Net over F4 — Digital
Digital (98, 126, 2738)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4126, 2738, F4, 28) (dual of [2738, 2612, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4126, 4095, F4, 28) (dual of [4095, 3969, 29]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4126, 4095, F4, 28) (dual of [4095, 3969, 29]-code), using
(98, 98+28, 528283)-Net in Base 4 — Upper bound on s
There is no (98, 126, 528284)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7237 059383 433640 946244 387405 782085 227414 957944 617916 010022 187229 848993 342300 > 4126 [i]