Best Known (45, 45+31, s)-Nets in Base 9
(45, 45+31, 344)-Net over F9 — Constructive and digital
Digital (45, 76, 344)-net over F9, using
- trace code for nets [i] based on digital (7, 38, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(45, 45+31, 410)-Net over F9 — Digital
Digital (45, 76, 410)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(976, 410, F9, 31) (dual of [410, 334, 32]-code), using
- 28 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0, 1, 20 times 0) [i] based on linear OA(974, 380, F9, 31) (dual of [380, 306, 32]-code), using
- trace code [i] based on linear OA(8137, 190, F81, 31) (dual of [190, 153, 32]-code), using
- extended algebraic-geometric code AGe(F,158P) [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- trace code [i] based on linear OA(8137, 190, F81, 31) (dual of [190, 153, 32]-code), using
- 28 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0, 1, 20 times 0) [i] based on linear OA(974, 380, F9, 31) (dual of [380, 306, 32]-code), using
(45, 45+31, 47403)-Net in Base 9 — Upper bound on s
There is no (45, 76, 47404)-net in base 9, because
- 1 times m-reduction [i] would yield (45, 75, 47404)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 370079 035787 045717 838749 234433 585171 572708 788324 295492 894483 537601 079329 > 975 [i]