MinT - Best Known (147−90, 147, s)-Nets in Base 8

Best Known (147−90, 147, s)-Nets in Base 8

(147−90, 147, 98)-Net over F₈ — Constructive and digital

Digital (57, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 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]

(147−90, 147, 144)-Net over F₈ — Digital

Digital (57, 147, 144)-net over F₈, using

t-expansion [i] based on digital (45, 147, 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]

(147−90, 147, 2216)-Net in Base 8 — Upper bound on s

There is no (57, 147, 2217)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 742718 892304 241165 684562 973920 882250 902010 654449 072227 484211 843363 064037 900312 901626 678077 923232 541027 043724 561997 490854 812492 566912 > 8¹⁴⁷ [i]