MinT - Best Known (162−114, 162, s)-Nets in Base 8

Best Known (162−114, 162, s)-Nets in Base 8

(162−114, 162, 98)-Net over F₈ — Constructive and digital

Digital (48, 162, 98)-net over F₈, using

t-expansion [i] based on 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]

(162−114, 162, 144)-Net over F₈ — Digital

Digital (48, 162, 144)-net over F₈, using

t-expansion [i] based on digital (45, 162, 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]

(162−114, 162, 1127)-Net in Base 8 — Upper bound on s

There is no (48, 162, 1128)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 207 999153 717527 754488 781157 105684 611292 015345 233066 943146 576643 948686 024529 566983 105097 387089 802899 398192 106984 757667 362816 029940 279113 249196 307064 > 8¹⁶² [i]