Best Known (120, 120+33, s)-Nets in Base 4
(120, 120+33, 1048)-Net over F4 — Constructive and digital
Digital (120, 153, 1048)-net over F4, using
- 41 times duplication [i] based on digital (119, 152, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 38, 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, 38, 262)-net over F256, using
(120, 120+33, 3682)-Net over F4 — Digital
Digital (120, 153, 3682)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4153, 3682, F4, 33) (dual of [3682, 3529, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 4124, F4, 33) (dual of [4124, 3971, 34]-code), using
- construction XX applied to Ce(32) ⊂ Ce(28) ⊂ Ce(26) [i] based on
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4121, 4096, F4, 27) (dual of [4096, 3975, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(45, 25, F4, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(32) ⊂ Ce(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4153, 4124, F4, 33) (dual of [4124, 3971, 34]-code), using
(120, 120+33, 1188454)-Net in Base 4 — Upper bound on s
There is no (120, 153, 1188455)-net in base 4, because
- 1 times m-reduction [i] would yield (120, 152, 1188455)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 32 592628 730172 633741 824844 247844 442854 396388 372649 120603 950191 781561 911915 362347 907281 160234 > 4152 [i]