MinT - Best Known (164−127, 164, s)-Nets in Base 8

Best Known (164−127, 164, s)-Nets in Base 8

(164−127, 164, 98)-Net over F₈ — Constructive and digital

Digital (37, 164, 98)-net over F₈, using

net from sequence [i] based on digital (37, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(164−127, 164, 121)-Net over F₈ — Digital

Digital (37, 164, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(164−127, 164, 714)-Net in Base 8 — Upper bound on s

There is no (37, 164, 715)-net in base 8, because

1 times m-reduction [i] would yield (37, 163, 715)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1705 433719 689758 576527 519707 740763 731390 240389 367389 287215 012578 741843 079659 785812 102764 953614 606420 884756 664131 181181 776754 552283 642426 769559 165504 > 8¹⁶³ [i]