Best Known (20, 20+25, s)-Nets in Base 81
(20, 20+25, 370)-Net over F81 — Constructive and digital
Digital (20, 45, 370)-net over F81, using
- t-expansion [i] based on digital (16, 45, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(20, 20+25, 477)-Net over F81 — Digital
Digital (20, 45, 477)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8145, 477, F81, 25) (dual of [477, 432, 26]-code), using
- 103 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 28 times 0, 1, 69 times 0) [i] based on linear OA(8141, 370, F81, 25) (dual of [370, 329, 26]-code), using
- extended algebraic-geometric code AGe(F,344P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- 103 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 28 times 0, 1, 69 times 0) [i] based on linear OA(8141, 370, F81, 25) (dual of [370, 329, 26]-code), using
(20, 20+25, 657727)-Net in Base 81 — Upper bound on s
There is no (20, 45, 657728)-net in base 81, because
- 1 times m-reduction [i] would yield (20, 44, 657728)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 940467 113619 403799 376074 150017 440350 157098 587207 581848 689062 562118 514811 401146 593281 > 8144 [i]