Best Known (133, 133+40, s)-Nets in Base 4
(133, 133+40, 1040)-Net over F4 — Constructive and digital
Digital (133, 173, 1040)-net over F4, using
- 41 times duplication [i] based on digital (132, 172, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 43, 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, 43, 260)-net over F256, using
(133, 133+40, 2424)-Net over F4 — Digital
Digital (133, 173, 2424)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4173, 2424, F4, 40) (dual of [2424, 2251, 41]-code), using
- 2250 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 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, 4 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, 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, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 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, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 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, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 73 times 0, 1, 77 times 0, 1, 79 times 0, 1, 82 times 0) [i] based on linear OA(440, 41, F4, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,4)), using
- dual of repetition code with length 41 [i]
- 2250 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 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, 4 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, 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, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 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, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 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, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 73 times 0, 1, 77 times 0, 1, 79 times 0, 1, 82 times 0) [i] based on linear OA(440, 41, F4, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,4)), using
(133, 133+40, 446671)-Net in Base 4 — Upper bound on s
There is no (133, 173, 446672)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 143 347269 686514 434234 102210 935782 388210 758595 332398 807553 293353 343069 055660 394618 030038 059109 787416 475036 > 4173 [i]