MinT - Best Known (159−100, 159, s)-Nets in Base 8

Best Known (159−100, 159, s)-Nets in Base 8

(159−100, 159, 98)-Net over F₈ — Constructive and digital

Digital (59, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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]

(159−100, 159, 144)-Net over F₈ — Digital

Digital (59, 159, 144)-net over F₈, using

t-expansion [i] based on digital (45, 159, 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]

(159−100, 159, 2040)-Net in Base 8 — Upper bound on s

There is no (59, 159, 2041)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 394932 862360 555572 654461 743838 372266 664124 984031 718700 126441 870725 025558 138817 229006 757010 924670 771335 228575 707282 609378 492093 829807 423217 517356 > 8¹⁵⁹ [i]