Best Known (235−52, 235, s)-Nets in Base 4
(235−52, 235, 1052)-Net over F4 — Constructive and digital
Digital (183, 235, 1052)-net over F4, using
- 1 times m-reduction [i] based on digital (183, 236, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 59, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 59, 263)-net over F256, using
(235−52, 235, 4106)-Net over F4 — Digital
Digital (183, 235, 4106)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4235, 4106, F4, 52) (dual of [4106, 3871, 53]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
(235−52, 235, 972430)-Net in Base 4 — Upper bound on s
There is no (183, 235, 972431)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3048 653378 073577 890516 310270 576283 091836 901799 168997 792477 970042 370785 197890 968833 785280 144459 042570 897394 035472 515953 647610 585981 729919 562760 > 4235 [i]