Best Known (179, 229, s)-Nets in Base 4
(179, 229, 1056)-Net over F4 — Constructive and digital
Digital (179, 229, 1056)-net over F4, using
- 41 times duplication [i] based on digital (178, 228, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 57, 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, 57, 264)-net over F256, using
(179, 229, 4233)-Net over F4 — Digital
Digital (179, 229, 4233)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4229, 4233, F4, 50) (dual of [4233, 4004, 51]-code), using
- 125 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 7 times 0, 1, 18 times 0, 1, 35 times 0, 1, 58 times 0) [i] based on linear OA(4223, 4102, F4, 50) (dual of [4102, 3879, 51]-code), using
- construction X applied to Ce(49) ⊂ Ce(48) [i] based on
- linear OA(4223, 4096, F4, 50) (dual of [4096, 3873, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4217, 4096, F4, 49) (dual of [4096, 3879, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(49) ⊂ Ce(48) [i] based on
- 125 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 7 times 0, 1, 18 times 0, 1, 35 times 0, 1, 58 times 0) [i] based on linear OA(4223, 4102, F4, 50) (dual of [4102, 3879, 51]-code), using
(179, 229, 1110110)-Net in Base 4 — Upper bound on s
There is no (179, 229, 1110111)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 744294 322592 355095 109304 420880 735932 343299 578143 225310 556099 725089 236526 735298 814109 517745 949632 446711 446579 231106 818440 025770 735001 203426 > 4229 [i]