MinT - Best Known (162−125, 162, s)-Nets in Base 8

Best Known (162−125, 162, s)-Nets in Base 8

(162−125, 162, 98)-Net over F₈ — Constructive and digital

Digital (37, 162, 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]

(162−125, 162, 121)-Net over F₈ — Digital

Digital (37, 162, 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]

(162−125, 162, 718)-Net in Base 8 — Upper bound on s

There is no (37, 162, 719)-net in base 8, because

1 times m-reduction [i] would yield (37, 161, 719)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26 844024 087193 101999 214889 463229 186424 322141 437417 793779 299633 111274 595361 376768 731991 482123 989340 623043 697264 770314 366800 634395 994969 070261 325468 > 8¹⁶¹ [i]