Best Known (183, 183+53, s)-Nets in Base 4
(183, 183+53, 1052)-Net over F4 — Constructive and digital
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
(183, 183+53, 3895)-Net over F4 — Digital
Digital (183, 236, 3895)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4236, 3895, F4, 53) (dual of [3895, 3659, 54]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 4103, F4, 53) (dual of [4103, 3867, 54]-code), using
- construction X applied to Ce(52) ⊂ Ce(50) [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]
- linear OA(4229, 4096, F4, 51) (dual of [4096, 3867, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(52) ⊂ Ce(50) [i] based on
- discarding factors / shortening the dual code based on linear OA(4236, 4103, F4, 53) (dual of [4103, 3867, 54]-code), using
(183, 183+53, 972430)-Net in Base 4 — Upper bound on s
There is no (183, 236, 972431)-net in base 4, because
- 1 times m-reduction [i] would yield (183, 235, 972431)-net in base 4, but
- 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]