Best Known (127, 127+38, s)-Nets in Base 4
(127, 127+38, 1040)-Net over F4 — Constructive and digital
Digital (127, 165, 1040)-net over F4, using
- 41 times duplication [i] based on digital (126, 164, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 41, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 41, 260)-net over F256, using
(127, 127+38, 2383)-Net over F4 — Digital
Digital (127, 165, 2383)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4165, 2383, F4, 38) (dual of [2383, 2218, 39]-code), using
- 2217 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 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, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 76 times 0, 1, 79 times 0, 1, 82 times 0, 1, 85 times 0) [i] based on linear OA(438, 39, F4, 38) (dual of [39, 1, 39]-code or 39-arc in PG(37,4)), using
- dual of repetition code with length 39 [i]
- 2217 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 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, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 76 times 0, 1, 79 times 0, 1, 82 times 0, 1, 85 times 0) [i] based on linear OA(438, 39, F4, 38) (dual of [39, 1, 39]-code or 39-arc in PG(37,4)), using
(127, 127+38, 447193)-Net in Base 4 — Upper bound on s
There is no (127, 165, 447194)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2187 336153 925193 336653 574629 987113 399341 090900 672438 999499 864182 461660 375081 802600 249198 422217 483188 > 4165 [i]