Best Known (21, 21+59, s)-Nets in Base 81
(21, 21+59, 370)-Net over F81 — Constructive and digital
Digital (21, 80, 370)-net over F81, using
- t-expansion [i] based on digital (16, 80, 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, 21+59, 23053)-Net in Base 81 — Upper bound on s
There is no (21, 80, 23054)-net in base 81, because
- 1 times m-reduction [i] would yield (21, 79, 23054)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 5 895981 420138 928458 473780 867166 205697 432667 301170 274418 827935 594153 650620 544862 558330 686556 484979 890877 269501 805436 240914 660011 356615 568359 099562 669281 > 8179 [i]