Best Known (235−53, 235, s)-Nets in Base 4
(235−53, 235, 1048)-Net over F4 — Constructive and digital
Digital (182, 235, 1048)-net over F4, using
- 1 times m-reduction [i] based on digital (182, 236, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 59, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 59, 262)-net over F256, using
(235−53, 235, 3789)-Net over F4 — Digital
Digital (182, 235, 3789)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4235, 3789, F4, 53) (dual of [3789, 3554, 54]-code), using
- discarding factors / shortening the dual code based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
- an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- discarding factors / shortening the dual code based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
(235−53, 235, 921938)-Net in Base 4 — Upper bound on s
There is no (182, 235, 921939)-net in base 4, because
- 1 times m-reduction [i] would yield (182, 234, 921939)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 762 166217 373331 755819 291326 830050 447496 774404 372598 652508 098301 047282 997148 982208 567476 878536 768223 848223 615260 711822 865421 430550 617187 849960 > 4234 [i]