Best Known (76, 76+27, s)-Nets in Base 5
(76, 76+27, 306)-Net over F5 — Constructive and digital
Digital (76, 103, 306)-net over F5, using
- 51 times duplication [i] based on digital (75, 102, 306)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (15, 28, 54)-net over F5, using
- trace code for nets [i] based on digital (1, 14, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- trace code for nets [i] based on digital (1, 14, 27)-net over F25, using
- digital (47, 74, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- digital (15, 28, 54)-net over F5, using
- (u, u+v)-construction [i] based on
(76, 76+27, 1563)-Net over F5 — Digital
Digital (76, 103, 1563)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5103, 1563, F5, 27) (dual of [1563, 1460, 28]-code), using
- 1459 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 48 times 0, 1, 52 times 0, 1, 54 times 0, 1, 59 times 0, 1, 62 times 0, 1, 66 times 0, 1, 71 times 0, 1, 75 times 0, 1, 80 times 0, 1, 86 times 0, 1, 91 times 0) [i] based on linear OA(527, 28, F5, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,5)), using
- dual of repetition code with length 28 [i]
- 1459 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 48 times 0, 1, 52 times 0, 1, 54 times 0, 1, 59 times 0, 1, 62 times 0, 1, 66 times 0, 1, 71 times 0, 1, 75 times 0, 1, 80 times 0, 1, 86 times 0, 1, 91 times 0) [i] based on linear OA(527, 28, F5, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,5)), using
(76, 76+27, 432078)-Net in Base 5 — Upper bound on s
There is no (76, 103, 432079)-net in base 5, because
- 1 times m-reduction [i] would yield (76, 102, 432079)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 197215 708495 743896 126861 426611 760214 087469 409316 356761 789892 487744 754445 > 5102 [i]