Best Known (21, 48, s)-Nets in Base 81
(21, 48, 370)-Net over F81 — Constructive and digital
Digital (21, 48, 370)-net over F81, using
- t-expansion [i] based on digital (16, 48, 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
(21, 48, 455)-Net over F81 — Digital
Digital (21, 48, 455)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8148, 455, F81, 27) (dual of [455, 407, 28]-code), using
- 80 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 21 times 0, 1, 52 times 0) [i] based on linear OA(8143, 370, F81, 27) (dual of [370, 327, 28]-code), using
- extended algebraic-geometric code AGe(F,342P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- 80 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 21 times 0, 1, 52 times 0) [i] based on linear OA(8143, 370, F81, 27) (dual of [370, 327, 28]-code), using
(21, 48, 562624)-Net in Base 81 — Upper bound on s
There is no (21, 48, 562625)-net in base 81, because
- 1 times m-reduction [i] would yield (21, 47, 562625)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 499802 806866 841592 949169 476319 594064 834540 138173 458336 069082 855997 162952 380575 711924 330001 > 8147 [i]