Best Known (239−52, 239, s)-Nets in Base 4
(239−52, 239, 1056)-Net over F4 — Constructive and digital
Digital (187, 239, 1056)-net over F4, using
- 1 times m-reduction [i] based on digital (187, 240, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 60, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
- trace code for nets [i] based on digital (7, 60, 264)-net over F256, using
(239−52, 239, 4414)-Net over F4 — Digital
Digital (187, 239, 4414)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4239, 4414, F4, 52) (dual of [4414, 4175, 53]-code), using
- 314 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0, 1, 95 times 0, 1, 111 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
- 314 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0, 1, 95 times 0, 1, 111 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
(239−52, 239, 1203607)-Net in Base 4 — Upper bound on s
There is no (187, 239, 1203608)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 780447 827654 290154 212320 767865 578524 603170 500538 272758 591106 524572 296272 568844 288803 613364 953154 758691 413037 930645 703455 875760 218815 581483 598800 > 4239 [i]