MinT - Best Known (161−114, 161, s)-Nets in Base 8

Best Known (161−114, 161, s)-Nets in Base 8

(161−114, 161, 98)-Net over F₈ — Constructive and digital

Digital (47, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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]

(161−114, 161, 144)-Net over F₈ — Digital

Digital (47, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(161−114, 161, 1085)-Net in Base 8 — Upper bound on s

There is no (47, 161, 1086)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 580387 503084 637373 121293 211521 901938 828944 372406 275578 622652 191360 501004 965749 894537 954652 224891 668581 068297 952117 912311 326179 750149 961938 096881 > 8¹⁶¹ [i]