Best Known (77−43, 77, s)-Nets in Base 81
(77−43, 77, 370)-Net over F81 — Constructive and digital
Digital (34, 77, 370)-net over F81, using
- t-expansion [i] based on digital (16, 77, 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
(77−43, 77, 672)-Net over F81 — Digital
Digital (34, 77, 672)-net over F81, using
(77−43, 77, 875579)-Net in Base 81 — Upper bound on s
There is no (34, 77, 875580)-net in base 81, because
- 1 times m-reduction [i] would yield (34, 76, 875580)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11 088305 939884 330001 168400 508629 075590 472783 563561 377384 804337 428515 760651 313415 429397 631710 100007 010689 763754 351348 660501 165812 198057 122302 334401 > 8176 [i]