Best Known (107, 107+33, s)-Nets in Base 4
(107, 107+33, 1036)-Net over F4 — Constructive and digital
Digital (107, 140, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 35, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
(107, 107+33, 1852)-Net over F4 — Digital
Digital (107, 140, 1852)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4140, 1852, F4, 33) (dual of [1852, 1712, 34]-code), using
- 1711 step Varšamov–Edel lengthening with (ri) = (9, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 48 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 69 times 0, 1, 73 times 0, 1, 76 times 0) [i] based on linear OA(433, 34, F4, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,4)), using
- dual of repetition code with length 34 [i]
- 1711 step Varšamov–Edel lengthening with (ri) = (9, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 48 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 69 times 0, 1, 73 times 0, 1, 76 times 0) [i] based on linear OA(433, 34, F4, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,4)), using
(107, 107+33, 385300)-Net in Base 4 — Upper bound on s
There is no (107, 140, 385301)-net in base 4, because
- 1 times m-reduction [i] would yield (107, 139, 385301)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 485684 335222 766315 212957 541848 108222 196901 425105 376980 506046 567691 817902 210767 226781 > 4139 [i]