MinT - Best Known (159−104, 159, s)-Nets in Base 8

Best Known (159−104, 159, s)-Nets in Base 8

(159−104, 159, 98)-Net over F₈ — Constructive and digital

Digital (55, 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]

(159−104, 159, 144)-Net over F₈ — Digital

Digital (55, 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]

(159−104, 159, 1635)-Net in Base 8 — Upper bound on s

There is no (55, 159, 1636)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 400466 232362 534499 933976 390452 312729 952968 744205 922041 520683 400486 669670 221411 343652 514719 575407 018579 976519 290458 621405 293085 034002 136987 864336 > 8¹⁵⁹ [i]